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Journal articles on the topic 'Metric mapping'

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Published: 7 July 2024

Last updated: 7 July 2024

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1

Filip, Alexandru-Darius. "Coincidence point theorems in some generalized metric spaces." Studia Universitatis Babes-Bolyai Matematica 68, no. 4 (December 30, 2023): 925–30. http://dx.doi.org/10.24193/subbmath.2023.4.18.

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"Let (X, d) be a complete dislocated metric space, (Y, ρ) be a semimetric space and f, g : X → Y be two mappings. Several coincidence point results are obtained for singlevalued and multivalued mappings. Keywords: Dislocated metric space, semimetric space, singlevalued and multivalued mapping, comparison function, comparison pair, lower semi-continuity, coincidence point displacement functional, iterative approximation of coincidence point, weakly Picard mapping, pre-weakly Picard mapping."

2

KAYA, MELTEM, and HASAN FURKAN. "Fixed point theorems for expansive mappings in Gp-metric spaces." Creative Mathematics and Informatics 26, no. 3 (2017): 297–308. http://dx.doi.org/10.37193/cmi.2017.03.07.

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In the present paper, we adopt the concept of expansive mapping in the context of Gp-metric spaces in a similar manner expansive mapping in metric spaces. Furthermore, we obtain some results on fixed points of expansive type mappings. Also, we prove some common fixed point results for expansive mappings by using the notion of weak compatibility in Gp-metric space. Our results generalize some comparable results in metric spaces and partial metric spaces to Gp-metric spaces. Moreover, some examples are introduced in order to support our new results.

3

Al Idrus, Ainun Sukmawati, Resmawan Resmawan, Muhammad Rezky Friesta Payu, Salmun K. Nasib, and Asriadi Asriadi. "Existence and Uniqueness of Fixed Point for Cyclic Mappings in Quasi-αb-Metric Spaces." InPrime: Indonesian Journal of Pure and Applied Mathematics 4, no. 1 (April 15, 2022): 58–64. http://dx.doi.org/10.15408/inprime.v4i1.24462.

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AbstractThe fixed point theory remains the most important and preferred topic studied in mathematical analysis. This study discusses sufficient conditions to prove a unique fixed point in quasi-αb-metric spaces with cyclic mapping. The analysis starts by showing fulfillment of the cyclic Banach contraction and proving the Cauchy sequence as a condition for proving a unique fixed point in quasi-αb-metric spaces with cyclic mapping. Furthermore, it's shown that the cyclic mappings, T have a unique fixed point in quasi-αb-metric spaces. Finally, an example is given to strengthen the proof of the theorems that have been done.Keywords: fixed point theory; Quasi -Metric spaces; Cyclic Banach Contraction; Cauchy sequence. AbstrakTeori titik tetap termasuk salah satu topik penting dan menarik untuk diteliti pada bidang analisis. Pada penelitian ini, dibahas tentang syarat cukup dalam membuktikan bahwa terdapat titik tetap tunggal dalam ruang quasi- b-metrik pada pemetaan siklik. Analisis diawali dengan menunjukkan pemenuhan kondisi kontraksi Banach siklik dan pembuktian barisan Cauchy sebagai syarat pembuktian bahwa terdapat titik tetap tunggal pada pemetaan siklik dalam ruang quasi- b-metrik. Selanjutnya ditunjukkan bahwa pemetaan siklik memiliki titik tetap tunggal dalam ruang quasi b-metrik. Terakhir, diberikan contoh untuk memperkuat pembuktian teorema yang telah dilakukan.Kata Kunci: teori titik tetap; ruang Quasi -Metrik; Kontraksi Banach Siklik; barisan Cauchy.

4

Zhukovskaia, Tatiana, and Elena Pluzhnikova. "The set of regularity of a multivalued mapping in a space with a vector-valued metric." Tambov University Reports. Series: Natural and Technical Sciences, no. 125 (2019): 39–46. http://dx.doi.org/10.20310/1810-0198-2019-24-125-39-46.

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We consider multivalued mappings acting in spaces with a vector-valued metric. A vector-valued metric is understood as a mapping satisfying the axioms “of an ordinary metric” with values in the cone of a linear normed space. The concept of the regularity set of a multivalued mapping is defined. A set of regularity is used in the study of inclusions in spaces with a vector-valued metric.

5

Yeşilkaya, Seher Sultan, and Cafer Aydın. "Fixed Point Results of Expansive Mappings in Metric Spaces." Mathematics 8, no. 10 (October 16, 2020): 1800. http://dx.doi.org/10.3390/math8101800.

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In this study, we introduce the concept of θ-expansive mapping in ordered metric spaces and prove a fixed point theorem for such mappings. We give some fixed point results for θ-expansive mapping in metric spaces and prove fixed point theorems for such mappings. These results extend the main results of many comparable results from the current literature. We also obtain a common fixed point theorem of two weakly compatible mappings in metric spaces. Finally, the examples are presented to support the new theorems and results proved.

6

Chen, Peng, Bin Meng, and Xiaohui Ba. "L-Quasi (Pseudo)-Metric in L-Fuzzy Set Theory." Mathematics 11, no. 14 (July 18, 2023): 3152. http://dx.doi.org/10.3390/math11143152.

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The aim of this paper is to focus on the metrization question in L-fuzzy sets. Firstly, we put forward an L-quasi (pseudo)-metric on the completely distributive lattice LX by comparing some existing lattice-valued metrics with the classical metric and show a series of its related properties. Secondly, we present two topologies: ψp and ζp, generated by an L-quasi-metric p with different spherical mappings, and prove ψp=ζp′ if p is further an L-pseudo-metric on LX. Thirdly, we characterize an equivalent form of L-pseudo-metric in terms of a class of mapping clusters and acquire several satisfactory results. Finally, based on this kind of L-metric, we assert that, on LX, a Yang–Shi metric topology is Q−CI, but an Erceg metric topology is not always so.

7

Sunarsini, S., S. Sadjidon, and Annisa Rahmita. "Weakly Contractive Mapping and Weakly Kannan Mapping in Partial Metric Space." Jurnal ILMU DASAR 20, no. 1 (January 22, 2019): 33. http://dx.doi.org/10.19184/jid.v20i1.6782.

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In the article the concept of metric space could be expanded, one of which is a partial metric space. In the metric space, the distance of a point to itself is equal to zero, while in the partial metric space need not be equal to zero.The concept of partial metric space is used to modify Banach's contraction principle. In this paper, we discuss weakly contractive mapping and weakly Kannan mapping which are extensions of Banach's contraction principle to partial metric space together some related examples. Additionally, we discuss someLemmas which are shows an analogy between Cauchy sequences in partial metric space with Cauchy sequences in metric space and analogy between the complete metric space and the complete partial metric space. Keywords: Cellulose metric space, partial metric space, weakly contraction mapping, weakly Kannan mapping.

8

Chauhan, Surjeet Singh, and Vishal Gupta. "Banach contraction theorem on fuzzy cone b-metric space." Journal of Applied Research and Technology 18, no. 4 (August 30, 2020): 154–60. http://dx.doi.org/10.22201/icat.24486736e.2020.18.4.1188.

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In the present paper the notion of fuzzy cone b -metric space has been introduced. Here we have defined fuzzy cone b -contractive mapping, and Banach contraction theorem for single mapping and pair of mappings has been proved in the setting of fuzzy cone b -metric space.

9

Ninsri, Aphinat, and Wutiphol Sintunavarat. "Approximation fixed theorems for α-partial weakly Zamfirescu mappings with application to homotopy invariance." Filomat 30, no. 7 (2016): 1941–56. http://dx.doi.org/10.2298/fil1607941n.

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In this paper, we introduce the concept of ?-partial weakly Zamfirescu mappings and give some approximate fixed point results for this mapping in ?-complete metric spaces. We also give some approximate fixed point results in ?-complete metric space endowed with an arbitrary binary relation and approximate fixed point results in ?-complete metric space endowed with graph. As application, we give homotopy results for ?-partial weakly Zamfirescu mapping.

10

Malahayati, Malahayati. "Ketunggalan Titik Tetap di Ruang Dislocated Quasi B-Metrik pada Pemetaan Siklik." Jurnal Matematika "MANTIK" 3, no. 1 (October 26, 2017): 39–43. http://dx.doi.org/10.15642/mantik.2017.3.1.39-43.

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The quasi b-metric dislocated space (dqb-metric space) was first introduced by Klin-eam and Suanoom in 2015. They had been proven the uniqueness of the fixed point in the dqb-metric space on cyclic mapping that provides the cyclic Banach contraction conditions. Furthermore, in 2016 Dolicanin et al showed that the fixed point singularity properties in the dqb-metric space can be proven without requiring the mapping to satisfy the cyclic metrics Banach contraction conditions. Both statements are proved equivalent in this paper.

11

Malahayati, Malahayati. "ANALISIS BEBERAPA TEOREMA KETUNGGALAN TITIK TETAP DI RUANG METRIK MULTIPLIKATIF (MULTIPLICATIVE METRIC SPACES)." Journal of Fundamental Mathematics and Applications (JFMA) 1, no. 1 (June 30, 2018): 22. http://dx.doi.org/10.14710/jfma.v1i1.5.

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This research was conducted to analyze several theorems about fixed point uniqueness on multiplicative metric space. Firstly, the proof of fixed point uniqueness theorem on complete multiplicative metric space is analyzed with involving multiplicative continuous functions. Then, several fixed point uniqueness theorems is analyzed without involving multiplicative continuous functions. The proof of fixed point uniqueness theorem on complete multiplicative metric space with involving multiplicative continuous functions can be done without requirement of contraction multiplicative mapping. If this mapping is satisfying a condition with involving multiplicative continuous functions then it was proven that it had the unique fixed point. Furthermore, the proof of fixed point uniqueness theorem on complete multiplicative metric space without involving multiplicative continuous functions can be done by requiring the mapping is contraction.

12

Al-Bundi, Salwa S. "A Fixed Point Theorem for L-Contraction in Generalized D-Metric Spaces." Baghdad Science Journal 5, no. 3 (September 7, 2008): 457–59. http://dx.doi.org/10.21123/bsj.2008.5.3.457-459.

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We define L-contraction mapping in the setting of D-metric spaces analogous to L-contraction mappings [1] in complete metric spaces. Also, give a definition for general D- matric spaces.And then prove the existence of fixed point for more general class of mappings in generalized D-metric spaces.

13

Zimmerman, Scott. "Sobolev Extensions of Lipschitz Mappings into Metric Spaces." International Mathematics Research Notices 2019, no. 8 (August 21, 2017): 2241–65. http://dx.doi.org/10.1093/imrn/rnx201.

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Abstract Wenger and Young proved that the pair $(\mathbb{R}^m,\mathbb{H}^n)$ has the Lipschitz extension property for $m \leq n$ where $\mathbb{H}^n$ is the sub-Riemannian Heisenberg group. That is, for some $C>0$, any $L$-Lipschitz map from a subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ can be extended to a $CL$-Lipschitz mapping on $\mathbb{R}^m$. In this article, we construct Sobolev extensions of such Lipschitz mappings with no restriction on the dimension $m$. We prove that any Lipschitz mapping from a compact subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ may be extended to a Sobolev mapping on any bounded domain containing the set. More generally, we prove this result in the case of mappings into any Lipschitz $(n-1)$-connected metric space.

14

Yang, Songlin, and Xun Ge. "so-metrizable spaces and images of metric spaces." Open Mathematics 19, no. 1 (January 1, 2021): 1145–52. http://dx.doi.org/10.1515/math-2021-0082.

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Abstract so-metrizable spaces are a class of important generalized metric spaces between metric spaces and s n sn -metrizable spaces where a space is called an so-metrizable space if it has a σ \sigma -locally finite so-network. As the further work that attaches to the celebrated Alexandrov conjecture, it is interesting to characterize so-metrizable spaces by images of metric spaces. This paper gives such characterizations for so-metrizable spaces. More precisely, this paper introduces so-open mappings and uses the “Pomomarev’s method” to prove that a space X X is an so-metrizable space if and only if it is an so-open, compact-covering, σ \sigma -image of a metric space, if and only if it is an so-open, σ \sigma -image of a metric space. In addition, it is shown that so-open mapping is a simplified form of s n sn -open mapping (resp. 2-sequence-covering mapping if the domain is metrizable). Results of this paper give some new characterizations of so-metrizable spaces and establish some equivalent relations among so-open mapping, s n sn -open mapping and 2-sequence-covering mapping, which further enrich and deepen generalized metric space theory.

15

Phuengrattana, Withun. "On the generalized asymptotically nonspreading mappings in convex metric spaces." Applied General Topology 18, no. 1 (April 3, 2017): 117. http://dx.doi.org/10.4995/agt.2017.6578.

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<p>In this article, we propose a new class of nonlinear mappings, namely, generalized asymptotically nonspreading mapping, and prove the existence of fixed points for such mapping in convex metric spaces. Furthermore, we also obtain the demiclosed principle and a delta-convergence theorem of Mann iteration for generalized asymptotically nonspreading mappings in CAT(0) spaces.</p>

16

MOHAPATRA, MANAS RANJAN, and SWADESH KUMAR SAHOO. "MAPPING PROPERTIES OF A SCALE INVARIANT CASSINIAN METRIC AND A GROMOV HYPERBOLIC METRIC." Bulletin of the Australian Mathematical Society 97, no. 1 (August 18, 2017): 141–52. http://dx.doi.org/10.1017/s0004972717000570.

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We consider a scale invariant Cassinian metric and a Gromov hyperbolic metric. We discuss a distortion property of the scale invariant Cassinian metric under Möbius maps of a punctured ball onto another punctured ball. We obtain a modulus of continuity of the identity map from a domain equipped with the scale invariant Cassinian metric (or the Gromov hyperbolic metric) onto the same domain equipped with the Euclidean metric. Finally, we establish the quasi-invariance properties of both metrics under quasiconformal maps.

17

Salimi, Peyman, Calogero Vetro, and Pasquale Vetro. "Some new fixed point results in non-Archimedean fuzzy metric spaces." Nonlinear Analysis: Modelling and Control 18, no. 3 (July 25, 2013): 344–58. http://dx.doi.org/10.15388/na.18.3.14014.

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In this paper, we introduce the notions of fuzzy (α,β,ϕ)-contractive mapping, fuzzy α-φ-ψ-contractive mapping and fuzzy α-β-contractive mapping and establish some results of fixed point for this class of mappings in the setting of non-Archimedean fuzzy metric spaces. The results presented in this paper generalize and extend some recent results in fuzzy metric spaces. Also, some examples are given to support the usability of our results.

18

Hassanzadeasl, Jalal. "Common Fixed Point Theorems for α-ψ-Contractive Type Mappings." International Journal of Analysis 2013 (April 11, 2013): 1–7. http://dx.doi.org/10.1155/2013/654659.

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Recently, Samet et al. (2012) introduced the notion of α-ψ-contractive type mappings. They established some fixed point theorems for these mappings in complete metric spaces. In this paper, we introduce the notion of a coupled α-ψ-contractive mapping and give a common fixed point result about the mapping. Also, we give a result of common fixed points of some coupled self-maps on complete metric spaces satisfying a contractive condition.

19

Zoto, Kastriot, Vesna Šešum-Čavić, Mirjana Pantović, Vesna Todorčević, Marsela Zoto, and Stojan Radenović. "A Unified Approach and Related Fixed-Point Theorems for Suzuki Contractions." Symmetry 16, no. 6 (June 13, 2024): 739. http://dx.doi.org/10.3390/sym16060739.

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This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics.

20

Kutbi, Marwan Amin, and Wutiphol Sintunavarat. "On the weakly(α, ψ, ξ)-contractive condition for multi-valued operators in metric spaces and related fixed point results." Open Mathematics 14, no. 1 (January 1, 2016): 167–80. http://dx.doi.org/10.1515/math-2016-0013.

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AbstractThe aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ)-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.

21

Shukla, Satish, Ishak Altun, and Ravindra Sen. "Fixed Point Theorems and Asymptotically Regular Mappings in Partial Metric Spaces." ISRN Computational Mathematics 2013 (May 23, 2013): 1–6. http://dx.doi.org/10.1155/2013/602579.

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The notion of asymptotically regular mapping in partial metric spaces is introduced, and a fixed point result for the mappings of this class is proved. Examples show that there are cases when new results can be applied, while old ones (in metric space) cannot. Some common fixed point theorems for sequence of mappings in partial metric spaces are also proved which generalize and improve some known results in partial metric spaces.

22

Phuengrattana, Withun, and Suthep Suantai. "Strong Convergence Theorems for a Countable Family of Nonexpansive Mappings in Convex Metric Spaces." Abstract and Applied Analysis 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/929037.

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We introduce a new modified Halpern iteration for a countable infinite family of nonexpansive mappings{Tn}in convex metric spaces. We prove that the sequence{xn}generated by the proposed iteration is an approximating fixed point sequence of a nonexpansive mapping when{Tn}satisfies the AKTT-condition, and strong convergence theorems of the proposed iteration to a common fixed point of a countable infinite family of nonexpansive mappings in CAT(0) spaces are established under AKTT-condition and the SZ-condition. We also generalize the concept ofW-mapping for a countable infinite family of nonexpansive mappings from a Banach space setting to a convex metric space and give some properties concerning the common fixed point set of this family in convex metric spaces. Moreover, by using the concept ofW-mappings, we give an example of a sequence of nonexpansive mappings defined on a convex metric space which satisfies the AKTT-condition. Our results generalize and refine many known results in the current literature.

23

Fulga, Andreea, and Erdal Karapınar. "Revisiting of some outstanding metric fixed point theorems via E-contraction." Analele Universitatii "Ovidius" Constanta - Seria Matematica 26, no. 3 (December 1, 2018): 73–98. http://dx.doi.org/10.2478/auom-2018-0034.

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AbstractIn this paper, we introduce the notion of α-ψ-contractive mapping of type E, to remedy of the weakness of the existing contraction mappings. We investigate the existence and uniqueness of a fixed point of such mappings. We also list some examples to illustrate our results that unify and generalize the several well-known results including the famous Banach contraction mapping principle.

24

Ugwunnadi, Godwin C., Chinedu Izuchukwu, and Oluwatosin T. Mewomo. "Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space." Journal of Applied Analysis 26, no. 2 (December 1, 2020): 221–29. http://dx.doi.org/10.1515/jaa-2020-2017.

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AbstractIn this paper, we introduce and study an Ishikawa-type iteration process for the class of generalized hemicontractive mappings in 𝑝-uniformly convex metric spaces, and prove both Δ-convergence and strong convergence theorems for approximating a fixed point of generalized hemicontractive mapping in complete 𝑝-uniformly convex metric spaces. We give a surprising example of this class of mapping that is not a hemicontractive mapping. Our results complement, extend and generalize numerous other recent results in CAT(0) spaces.

25

Rhoades, B. E. "A common fixed point theorem for a sequence of fuzzy mappings." International Journal of Mathematics and Mathematical Sciences 18, no. 3 (1995): 447–49. http://dx.doi.org/10.1155/s0161171295000561.

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We obtain a common fixed point theorem for a sequence of fuzzy mappings, satisfying a contractive definition more general than that of Lee, Lee, Cho and Kim [2].Let(X,d)be a complete linear metric space. A fuzzy setAinXis a function fromXinto[0,1]. Ifx∈X, the function valueA(x)is called the grade of membership ofXinA. Theα-level set ofA,Aα:={x:A(x)≥α, if α∈(0,1]}, andA0:={x:A(x)>0}¯.W(X)denotes the collection of all the fuzzy setsAinXsuch thatAαis compact and convex for eachα∈[0,1]andsupx∈XA(x)=1. ForA,B∈W(X),A⊂BmeansA(x)≤B(x)for eachx∈X. ForA,B∈W(X),α∈[0,1], definePα(A,B)=infx∈Aα,y∈Bαd(x,y), P(A,B)=supαPα(A,B), D(A,B)=supαdH(Aα,Bα), wheredHis the Hausdorff metric induced by the metricd. We notc thatPαis a nondecrcasing function ofαandDis a metric onW(X).LetXbe an arbitrary set,Yany linear metric space.Fis called a fuzzy mapping ifFis a mapping from the setXintoW(Y).In earlier papers the author and Bruce Watson, [3] and [4], proved some fixed point theorems for some mappings satisfying a very general contractive condition. In this paper we prove a fixed point theorem for a sequence of fuzzy mappings satisfying a special case of this general contractive condition. We shall first prove the theorem, and then demonstrate that our definition is more general than that appearing in [2].LetDdenote the closure of the range ofd. We shall be concerned with a functionQ, defined ondand satisfying the following conditions:(a) 0<Q(s)<s for each s∈D\{0} and Q(0)=0(b) Q is nondecreasing on D, and(c) g(s):=s/(s−Q(s)) is nonincreasing on D\{0}LEMMA 1. [1] Let(X,d)be a complete linear metric space,Fa fuzzy mapping fromXintoW(X)andx0∈X. Then there exists anx1∈Xsuch that{x1}⊂F(x0).

26

Ren, Yijie, Junlei Li, and Yanrong Yu. "Common Fixed Point Theorems for Nonlinear Contractive Mappings in Dislocated Metric Spaces." Abstract and Applied Analysis 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/483059.

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In 1986, Matthews generalized Banach contraction mapping theorem in dislocated metric space that is a wider space than metric space. In this paper, we established common fixed point theorems for a class of contractive mappings. Our results extend the corresponding ones of other authors in dislocated metric spaces.

27

Bergman, George. "Mapping radii of metric spaces." Pacific Journal of Mathematics 236, no. 2 (June 1, 2008): 223–61. http://dx.doi.org/10.2140/pjm.2008.236.223.

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Gebru, Yohannes, and Yitages Negede. "Common Best Proximity Point Theorems for Generalized Proximal Weakly Contractive Mappings in b-Metric Space." Abstract and Applied Analysis 2022 (August 24, 2022): 1–11. http://dx.doi.org/10.1155/2022/5982401.

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In this paper, common best proximity point theorems for weakly contractive mapping in b-metric spaces in the cases of nonself-mappings are proved; we introduced the notion of generalized proximal weakly contractive mappings in b-metric spaces and proved the existence and uniqueness of common best proximity point for these mappings in complete b-metric spaces. We also included some supporting examples that our finding is more generalized with the references we used.

29

Mebawondu, Akindele Adebayo, Chinedu Izuchukwu, Hammed Anuoluwapo Abass, and Oluwatosin Temitope Mewomo. "Some results on generalized mean nonexpansive mapping in complete metric spaces." Boletim da Sociedade Paranaense de Matemática 40 (January 23, 2022): 1–16. http://dx.doi.org/10.5269/bspm.44174.

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In this paper, we obtain sufficient conditions for the existence of a unique fixed point of $T$- mean nonexpansive mapping and an integral type of $T$- mean nonexpansive mapping. We also obtain sufficient conditions for the existence of coincidence point and common fixed point for a Jungck-type mean nonexpansive mapping in the frame work of a complete metric space. Some examples of $T$-mean nonexpansive and Jungck-type mean nonexpansive mappings which are not mean nonexpansive mapping are given. The result obtained generalizes corresponding results in this direction in the literature.

30

Edraoui, Mohamed, Amine El koufi, and Mohamed Aamri. "On interpolative Hardy-Rogers type cyclic contractions." Applied General Topology 25, no. 1 (April 2, 2024): 117–24. http://dx.doi.org/10.4995/agt.2024.19885.

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Recently, Karapınar introduced a new Hardy-Rogers type contractive mapping using the concept of interpolation and proved a fixed point theorem in complete metric space. This new type of mapping, called "interpolative Hardy-Rogers type contractive mapping" is a generalization of Hardy-Rogers's fixed point theorem. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for cyclic mappings on complete metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.

31

Batsari, Umar, Poom Kumam, and Kanokwan Sitthithakerngkiet. "Some Globally Stable Fixed Points in b-Metric Spaces." Symmetry 10, no. 11 (October 30, 2018): 555. http://dx.doi.org/10.3390/sym10110555.

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In this paper, the existence and uniqueness of globally stable fixed points of asymptotically contractive mappings in complete b-metric spaces were studied. Also, we investigated the existence of fixed points under the setting of a continuous mapping. Furthermore, we introduce a contraction mapping that generalizes that of Banach, Kanan, and Chatterjea. Using our new introduced contraction mapping, we establish some results on the existence and uniqueness of fixed points. In obtaining some of our results, we assume that the space is associated with a partial order, and the b-metric function has the regularity property. Our results improve, and generalize some current results in the literature.

32

Mishra, Alok, Raed Shatnawi, Cagatay Catal, and Akhan Akbulut. "Techniques for Calculating Software Product Metrics Threshold Values: A Systematic Mapping Study." Applied Sciences 11, no. 23 (December 1, 2021): 11377. http://dx.doi.org/10.3390/app112311377.

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Several aspects of software product quality can be assessed and measured using product metrics. Without software metric threshold values, it is difficult to evaluate different aspects of quality. To this end, the interest in research studies that focus on identifying and deriving threshold values is growing, given the advantage of applying software metric threshold values to evaluate various software projects during their software development life cycle phases. The aim of this paper is to systematically investigate research on software metric threshold calculation techniques. In this study, electronic databases were systematically searched for relevant papers; 45 publications were selected based on inclusion/exclusion criteria, and research questions were answered. The results demonstrate the following important characteristics of studies: (a) both empirical and theoretical studies were conducted, a majority of which depends on empirical analysis; (b) the majority of papers apply statistical techniques to derive object-oriented metrics threshold values; (c) Chidamber and Kemerer (CK) metrics were studied in most of the papers, and are widely used to assess the quality of software systems; and (d) there is a considerable number of studies that have not validated metric threshold values in terms of quality attributes. From both the academic and practitioner points of view, the results of this review present a catalog and body of knowledge on metric threshold calculation techniques. The results set new research directions, such as conducting mixed studies on statistical and quality-related studies, studying an extensive number of metrics and studying interactions among metrics, studying more quality attributes, and considering multivariate threshold derivation.

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Petrov, Evgeniy, and Ruslan Salimov. "Quasisymmetric mappings in b-metric spaces." Ukrainian Mathematical Bulletin 18, no. 1 (March 9, 2021): 60–70. http://dx.doi.org/10.37069/1810-3200-2021-18-1-4.

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Considering quasisymmetric mappings between b-metric spaces we have found a new estimation for the ratio of diameters of two subsets which are images of two bounded subsets. This result generalizes the well-known Tukia-Vaisala inequality. The condition under which the image of a b-metric space under a quasisymmetric mapping is also a b-metric space is established. Moreover, the latter question is investigated for additive metric spaces.

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Krupka, Demeter, and Ján Brajerčík. "Schwarzschild Spacetimes: Topology." Axioms 11, no. 12 (December 4, 2022): 693. http://dx.doi.org/10.3390/axioms11120693.

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This paper is devoted to the geometric theory of a Schwarzschild spacetime, a basic objective in applications of the classical general relativity theory. In a broader sense, a Schwarzschild spacetime is a smooth manifold, endowed with an action of the special orthogonal group SO(3) and a Schwarzschild metric, an SO(3)-invariant metric field, satisfying the Einstein equations. We prove the existence of and find all Schwarzschild metrics on two topologically non-equivalent manifolds, R×(R3∖{(0,0,0)}) and S1×(R3∖{(0,0,0)}). The method includes a classification of SO(3)-invariant, time-translation invariant and time-reflection invariant metrics on R×(R3∖{(0,0,0)}) and a winding mapping of the real line R onto the circle S1. The resulting family of Schwarzschild metrics is parametrized by an arbitrary function and two real parameters, the integration constants. For any Schwarzschild metric, one of the parameters determines a submanifold, where the metric is not defined, the Schwarzschild sphere. In particular, the family admits a global metric whose Schwarzschild sphere is empty. These results transfer to S1×(R3∖{(0,0,0)}) by the winding mapping. All our assertions are derived independently of the signature of the Schwarzschild metric; the signature can be chosen as an independent axiom.

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Weng, Shengquan, and Quanxin Zhu. "Some Fixed-Point Theorems on Generalized Cyclic Mappings in B-Metric-Like Spaces." Complexity 2021 (August 28, 2021): 1–7. http://dx.doi.org/10.1155/2021/9042402.

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In this paper, it is concerned with the cyclic mapping in b-metric-like spaces. The definition of W -type cyclic mappings is proposed, and then, the existence-uniqueness of the fixed points of these cyclic mappings and the corresponding fixed point theorems are studied. In b-metric-like spaces, the promotion of the concept of cyclic mapping is an interesting topic; then, it is worthy to continue to this part of the promotion. On this basis, the concept of φ -type cyclic mapping is proposed in this article, and the existence-uniqueness of fixed-point problems and the corresponding fixed-point theorem are considered and studied. The results of this paper further generalize and extend some previous results.

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Güner, Elif, Vildan Çetkin, and Halis Aygün. "On Intuitionistic Fuzzy 2-Metric Spaces." ITM Web of Conferences 22 (2018): 01024. http://dx.doi.org/10.1051/itmconf/20182201024.

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In this study, we first recall the notion of an intuitionistic fuzzy 2-metric space and fundamental definitions with several illustrative examples. Then we define the notion of δ−chainable space and (δ,λ)−uniform locally contractive mapping between intuitionistic fuzzy 2-metric spaces. After that, by using the proposed concepts, we obtain a few fixed point theorems of self-mappings defined on this spaces.

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Jha, Pavan Kumar. "Historical Development of some Fixed Point Results in Metric Space." Annals of Pure and Applied Mathematics 26, no. 02 (2022): 79–89. http://dx.doi.org/10.22457/apam.v26n2a04884.

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In this paper, the historical account of fixed point results for single mapping in metric space has been provided. Though, there is a vast account of fixed point results for two or more mappings in the literature. It is mainly concentrated on single mapping due to our philosophical touch on Sthira Vindu (fixed point) and Kutastha Vindu in Vedanta philosophy.

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Zhukovskaia, Tatiana V., Wassim Merchela, and Andrey I. Shindiapin. "On coincidence points of mappings in generalized metric spaces." Russian Universities Reports. Mathematics, no. 129 (2020): 18–24. http://dx.doi.org/10.20310/2686-9667-2020-25-129-18-24.

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Abstract. Let 𝑋 be a space with ∞-metric 𝜌 (a metric with possibly inﬁnite value) and 𝑌 a space with ∞-distance 𝑑 satisfying the identity axiom. We consider the problem of coincidence point for mappings 𝐹,𝐺:𝑋→𝑌, i.e. the problem of existence of a solution for the equation 𝐹(𝑥)=𝐺(𝑥). We provide conditions of the existence of coincidence points in terms of a covering set for the mapping 𝐹 and a Lipschitz set for the mapping 𝐺 in the space 𝑋×𝑌. An 𝛼-covering set (𝛼>0) of the mapping 𝐹 is a set of (𝑥,𝑦) such that ∃𝑢∈𝑋 𝐹(𝑢)=𝑦, 𝜌(𝑥,𝑢)≤𝛼−1𝑑(𝐹(𝑥),𝑦), 𝜌(𝑥,𝑢)<∞, and a 𝛽 - Lipschitz set (𝛽≥0) for the mapping 𝐺 is a set of (𝑥,𝑦) such that ∀𝑢∈𝑋 𝐺(𝑢)=𝑦⇒𝑑(𝑦,𝐺(𝑥))≤𝛽𝜌(𝑢,𝑥). The new results are compared with the known theorems about coincidence points.

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Mousa, Maha, and Salwa Salman Abed. "Coincidence points in θ - metric spaceS." JOURNAL OF ADVANCES IN MATHEMATICS 20 (February 14, 2021): 50–55. http://dx.doi.org/10.24297/jam.v20i.8929.

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In this paper, inspired by the concept of metric space, two fixed point theorems for α−set-valued mapping T:₳ → CB(₳), h θ (Tp,Tq) ≤ α(dθ(p,q)) dθ(p,q), where α: (0,∞) → (0, 1] such that α(r) < 1, ∀ t ∈ [0,∞) ) are given in complete θ −metric and then extended for two mappings with R-weakly commuting property to obtain a common coincidence point.

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FUKHAR-UD-DIN, HAFIZ. "Existence and approximation of fixed points in convex metric spaces." Carpathian Journal of Mathematics 30, no. 2 (2014): 175–85. http://dx.doi.org/10.37193/cjm.2014.02.11.

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A fixed point theorem for a generalized nonexpansive mapping is established in a convex metric space introduced by Takahashi [A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142–149]. Our theorem generalizes simultaneously the fixed point theorem of Bose and Laskar [Fixed point theorems for certain class of mappings, Jour. Math. Phy. Sci., 19 (1985), 503–509] and the well-known fixed point theorem of Goebel and Kirk [A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171–174] on a nonlinear domain. The fixed point obtained is approximated by averaging Krasnosel’skii iterations of the mapping. Our results substantially improve and extend several known results in uniformly convex Banach spaces and CAT(0) spaces.

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Yue, Chen, H. M. Abu-Donia, H. A. Atia, Omnia M. A. Khater, Mona S. Bakry, Eman Safaa, and Mostafa M. A. Khater. "Weakly compatible fixed point theorem in intuitionistic fuzzy metric spaces." AIP Advances 13, no. 4 (April 1, 2023): 045113. http://dx.doi.org/10.1063/5.0147488.

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This study presents fundamental theorems, lemmas, and mapping definitions. There are three types of mappings: binary operators, compatible mappings, and sequentially continuous mappings. The symbols used to represent fuzzy metric spaces are intuitive. Icons were also used to prescribe a shared, linked fixed point in intuitionistic fuzzy metric space for two compatible and sequentially continuous mappings that satisfy ϕ-contractive conditions. To accomplish this, finding the intersection of both mappings was necessary.

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Jleli, Mohamed, Bessem Samet, Calogero Vetro, and Francesca Vetro. "Fixed Points for Multivalued Mappings inb-Metric Spaces." Abstract and Applied Analysis 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/718074.

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In 2012, Samet et al. introduced the notion ofα-ψ-contractive mapping and gave sufficient conditions for the existence of fixed points for this class of mappings. The purpose of our paper is to study the existence of fixed points for multivalued mappings, under anα-ψ-contractive condition of Ćirić type, in the setting of completeb-metric spaces. An application to integral equation is given.

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Devi, Sarita, Manoj Kumar, and Sushma Devi. "Some Fixed Point Theorems in S-metric Spaces via Simulation Function." Asian Research Journal of Mathematics 19, no. 9 (June 22, 2023): 13–24. http://dx.doi.org/10.9734/arjom/2023/v19i9695.

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We introduce the concept of generalized \(\beta\) - \(\gamma\) - Z contraction mapping with respect to a simulation function ξ and study the existence of fixed points for such mappings in complete -metric spaces. Further, we extend it to partially ordered complete -metric spaces.

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Al-Yaari, Abdullah, Hamzah Sakidin, Yousif Alyousifi, and Qasem Al-Tashi. "Fixed point theorem between cone metric space and quasi-cone metric space." Indonesian Journal of Electrical Engineering and Computer Science 25, no. 1 (January 1, 2022): 540. http://dx.doi.org/10.11591/ijeecs.v25.i1.pp540-549.

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This study involves new notions of continuity of mapping between quasi-cone metrics spaces (QCMSs), cone metric spaces (CMSs), and vice versa. The relation between all notions of continuity were thoroughly studied and supported with the help of examples. In addition, these new continuities were compared with various types of continuities of mapping between two QCMSs. The continuity types are 𝒇𝒇-continuous, 𝒃𝒃-continuous, 𝒇𝒃-continuous, and 𝒃𝒇-continuous. The results demonstrated that the new notions of continuity could be generalized to the continuity of mapping between two QCMSs. It also showed a fixed point for this continuity map between a complete Hausdorff CMS and QCMS. Overall, this study supports recent research results.

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Manjusha P.Gandhi, Anushree A. Aserkar,. "Expansion Mapping Theorem for Four Mappings Satisfying Common Limit in the Range Property in b-Metric Space." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 6 (April 5, 2021): 2354–59. http://dx.doi.org/10.17762/turcomat.v12i6.5284.

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In the present paper, for four weakly compatible mappings in pairs, an expansion mapping theorem has been developed in b-metric space, meeting common limit range property. We proved this theorem without using the b-metric space's completeness condition. The result is an extension and generalization of several metric space results available. To confirm the finding, a suitable example is also discussed.

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Babu, G. V. R., Durga Sailaja, and G. Srichandana. "Strong coupled proximal points of cyclic coupled proximal mappings using Ck-class functions in S-metric spaces." Filomat 36, no. 3 (2022): 933–44. http://dx.doi.org/10.2298/fil2203933b.

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In this paper, we introduce cyclic coupled proximal mapping in S-metric spaces using Ck-class functions and prove the existence of strong coupled proximal points of such mappings in complete S-metric spaces. Also, we provide an example in support of our main result.

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Liu, Zeqing, Lili Zhang, and Shin Min Kang. "On characterizations of fixed points." International Journal of Mathematics and Mathematical Sciences 27, no. 7 (2001): 391–97. http://dx.doi.org/10.1155/s0161171201007037.

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We give some necessary and sufficient conditions for the existence of fixed points of a family of self mappings of a metric space and we establish an equivalent condition for the existence of fixed points of a continuous compact mapping of a metric space.

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Vincent, Koech, Musundi W. Sammy, and Kinyanjui Jeremiah. "Derivation of Fixed-Point Theorem Using Expansive Mapping Approach." Asian Research Journal of Mathematics 19, no. 8 (June 7, 2023): 103–7. http://dx.doi.org/10.9734/arjom/2023/v19i8692.

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Application of Fixed-Point Theorem has tremendously increased in different areas of interest and research. Fixed Point Theorem presents that if T:X→X is a contraction mapping on a complete metric space (X, d) then there exists a unique fixed point in X. A lot has been done on application of contraction mapping in Fixed Point Theorem on metric spaces such as Cantor set with the contraction constant of 1/3 , the Sierpinski triangle also with contraction constant of 1/2 . On the other hand, a mapping T:X → X on (X, d) such that ∀x, y ∈ X: d(Tx, Ty) ≥ d (x, y) is called an expansive mapping. There are various types of expansive mappings such as; isometry expansive mapping, proper/strict expansive mapping and anti-contraction expansive mapping. From the available literature, Fixed Point Theorem has been derived using contraction mapping approach. In this paper, we establish that it is also possible to derive Fixed Point Theorem using expansive mapping approach.

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Marinov, Rumen Tsanev, and Diana Kirilova Nedelcheva. "Implicit mapping theorem for extended metric regularity in metric spaces." Ricerche di Matematica 62, no. 1 (December 12, 2012): 55–66. http://dx.doi.org/10.1007/s11587-012-0139-z.

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Balcerzak, M., S. A. Belov, and V. V. Chistyakov. "On Helly's principle for metric semigroup valued BV mappings to two real variables." Bulletin of the Australian Mathematical Society 66, no. 2 (October 2002): 245–57. http://dx.doi.org/10.1017/s0004972700040090.

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We introduce a concept of metric space valued mappings of two variables with finite total variation and define a counterpart of the Hardy space. Then we establish the following Helly type selection principle for mappings of two variables: Let X be a metric space and a commutative additive semigroup whose metric is translation invariant. Then an infinite pointwise precompact family of X-valued mappings on the closed rectangle of the plane, which is of uniformly bounded total variation, contains a pointwise convergent sequence whose limit is a mapping with finite total variation.