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Journal articles on the topic 'Mappings (Mathematics)'

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Published: 4 June 2021

Last updated: 29 July 2024

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1

Sarsak, Mohammad S. "Weak Forms of Continuity andcmd="newline"Associated Properties." International Journal of Mathematics and Mathematical Sciences 2008 (2008): 1–9. http://dx.doi.org/10.1155/2008/790964.

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We introduce slightly -continuous mapping and almost -open mapping and investigate the relationships between these mappings and related types of mappings, and also study some properties of these mappings.

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2

Li, Liulan, and Saminathan Ponnusamy. "Rotations and convolutions of harmonic convex mappings." Filomat 36, no. 11 (2022): 3845–60. http://dx.doi.org/10.2298/fil2211845l.

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In this paper, we mainly consider the convolutions of slanted half-plane mappings and strip mappings of the unit disk D. If f1 is a slanted half-plane mapping and f2 is a slanted half-plane mapping or a strip mapping, then we prove that f1 * f2 is convex in some direction if f1 * f2 is locally univalent in D. We also obtain two sufficient conditions for f1 * f2 to be locally univalent in D. Our results extend many of the recent results in this direction. Moreover, we consider a class of harmonic mappings including slanted half-plane mappings and strip mappings, and as a consequence, we prove that the any convex combination of such locally univalent and sense-preserving mappings is also convex.

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3

Gupta, Sanjeev, Shamshad Husain, and Vishnu Mishra. "Variational inclusion governed by αβ-H((.,.),(.,.))-mixed accretive mapping." Filomat 31, no. 20 (2017): 6529–42. http://dx.doi.org/10.2298/fil1720529g.

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In this paper, we look into a new concept of accretive mappings called ??-H((.,.),(.,.))-mixed accretive mappings in Banach spaces. We extend the concept of proximal-point mappings connected with generalized m-accretive mappings to the ??-H((.,.),(.,.))-mixed accretive mappings and discuss its characteristics like single-valuable and Lipschitz continuity. Some illustration are given in support of ??-H((.,.),(.,.))-mixed accretive mappings. Since proximal point mapping is a powerful tool for solving variational inclusion. Therefore, As an application of introduced mapping, we construct an iterative algorithm to solve variational inclusions and show its convergence with acceptable assumptions.

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4

Bridges, Douglas, and Ray Mines. "Sequentially continuous linear mappings in constructive analysis." Journal of Symbolic Logic 63, no. 2 (June 1998): 579–83. http://dx.doi.org/10.2307/2586851.

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A mapping u: X → Y between metric spaces is sequentially continuous if for each sequence (xn) converging to x ∈ X, (u(xn)) converges to u(x). It is well known in classical mathematics that a sequentially continuous mapping between metric spaces is continuous; but, as all proofs of this result involve the law of excluded middle, there appears to be a constructive distinction between sequential continuity and continuity. Although this distinction is worth exploring in its own right, there is another reason why sequential continuity is interesting to the constructive mathematician: Ishihara [8] has a version of Banach's inverse mapping theorem in functional analysis that involves the sequential continuity, rather than continuity, of the linear mappings; if this result could be upgraded by deleting the word “sequential”, then we could prove constructively the standard versions of the inverse mapping theorem and the closed graph theorem.Troelstra [9] showed that in Brouwer's intuitionistic mathematics (INT) a sequentially continuous mapping on a separable metric space is continuous. On the other hand, Ishihara [6, 7] proved constructively that the continuity of sequentially continuous mappings on a separable metric space is equivalent to a certain boundedness principle for subsets of ℕ; in the same paper, he showed that the latter principle holds within the recursive constructive mathematics (RUSS) of the Markov School. Since it is not known whether that principle holds within Bishop's constructive mathematics (BISH), of which INT and RUSS are models and which can be regarded as the constructive core of mathematics, the exploration of sequential continuity within BISH holds some interest.

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5

Joseph, S., R. Balakumar, and A. Swaminathan. "Fuzzy totally semi alpha-irresolute mappings." Boletim da Sociedade Paranaense de Matemática 41 (December 24, 2022): 1–7. http://dx.doi.org/10.5269/bspm.51341.

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The aim of this article is to introduce two new classes of mappings called fuzzy totally semi -irresolute mapping and fuzzy totally almost irresolute mapping. Moreover, their characterizations , examples and compositions of these mappings, their relationships between other fuzzy mappings are studied.

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6

Huang, Manzi, Antti Rasila, and Xiantao Wang. "Mapping problems for quasiregular mappings." Filomat 27, no. 2 (2013): 391–402. http://dx.doi.org/10.2298/fil1302391h.

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7

Gupta, Sanjeev, and Faizan Khan. "A class of Yosida inclusion and graph convergence on Yosida approximation mapping with an application." Filomat 37, no. 15 (2023): 4881–902. http://dx.doi.org/10.2298/fil2315881g.

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The proposed work is presented in two folds. The first aim is to deals with the new notion called generalized ?i?j-Hp(., ., ...)-accretive mappings that are the sum of two symmetric accretive mappings. It is an extension of ??-H(., .)-accretive mapping, studied and analyzed by Kazmi [18]. We define the proximalpoint mapping associated with generalized ?i?j-Hp(., ., ...)-accretive mapping and demonstrate aspects on single-valued property and Lipschitz continuity. The graph convergence of generalized ?i?j-Hp(., ., ...)- accretive mapping is discussed. Second aim is to introduce and study the generalized Yosida approximation mapping and Yosida inclusion problem. Next, we obtain the convergence on generalized Yosida approximation mappings by using the graph convergence of generalized ?i?j-Hp(., ., ...)-accretive mappings without using the convergence of its proximal-point mapping. As an application, we consider the Yosida inclusion problem in q-uniformly smooth Banach spaces and propose an iterative scheme connected with generalized Yosida approximation mapping of generalized ?i?j-Hp(., ., ...)-accretive mapping to find a solution of Yosida inclusion problem and discuss its convergence criteria under appropriate assumptions. Some examples are constructed and demonstrate few graphics for the convergence of proximal-point mapping as well as generalized Yosida approximation mapping linked with generalized ?i?j-Hp(., ., ...)-accretive mappings.

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8

Pavlíček, Libor. "Monotonically Controlled Mappings." Canadian Journal of Mathematics 63, no. 2 (April 1, 2011): 460–80. http://dx.doi.org/10.4153/cjm-2011-004-0.

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Abstract We study classes of mappings between finite and infinite dimensional Banach spaces that are monotone and mappings which are differences of monotone mappings (DM). We prove a Radó–Reichelderfer estimate for monotone mappings in finite dimensional spaces that remains valid for DM mappings. This provides an alternative proof of the Fréchet differentiability a.e. of DM mappings. We establish a Morrey-type estimate for the distributional derivative of monotone mappings. We prove that a locally DM mapping between finite dimensional spaces is also globally DM. We introduce and study a new class of the so-called UDM mappings between Banach spaces, which generalizes the concept of curves of finite variation.

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9

Chidume, C. E., K. R. Kazmi, and H. Zegeye. "Iterative approximation of a solution of a general variational-like inclusion in Banach spaces." International Journal of Mathematics and Mathematical Sciences 2004, no. 22 (2004): 1159–68. http://dx.doi.org/10.1155/s0161171204209395.

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We introduce a class ofη-accretive mappings in a real Banach space and show that theη-proximal point mapping forη-m-accretive mapping is Lipschitz continuous. Further, we develop an iterative algorithm for a class of general variational-like inclusions involvingη-accretive mappings in real Banach space, and discuss its convergence criteria. The class ofη-accretive mappings includes several important classes of operators that have been studied by various authors.

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10

Chen, Jiawei, Zhongping Wan, Liuyang Yuan, and Yue Zheng. "Approximation of Fixed Points of Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–23. http://dx.doi.org/10.1155/2011/420192.

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We introduce a concept of weak Bregman relatively nonexpansive mapping which is distinct from Bregman relatively nonexpansive mapping. By using projection techniques, we construct several modification of Mann type iterative algorithms with errors and Halpern-type iterative algorithms with errors to find fixed points of weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings in Banach spaces. The strong convergence theorems for weak Bregman relatively nonexpansive mappings and Bregman relatively nonexpansive mappings are derived under some suitable assumptions. The main results in this paper develop, extend, and improve the corresponding results of Matsushita and Takahashi (2005) and Qin and Su (2007).

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11

KAEWKHAO, A., C. KLANGPRAPHAN, and B. PANYANAK. "Fixed points of Osilike-Berinde-G-nonexpansive mappings in metric spaces endowed with graphs." Carpathian Journal of Mathematics 37, no. 2 (June 9, 2021): 311–23. http://dx.doi.org/10.37193/cjm.2021.02.16.

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"In this paper, we introduce the notion of Osilike-Berinde-G-nonexpansive mappings in metric spaces and show that every Osilike-Berinde-G-nonexpansive mapping with nonempty fixed point set is a G-quasinonexpansive mapping. We also prove the demiclosed principle and apply it to obtain a fixed point theorem for Osilike-Berinde-G-nonexpansive mappings. Strong and \Delta-convergence theorems of the Ishikawa iteration process for G-quasinonexpansive mappings are also discussed."

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12

Xu, Hong-Kun. "Diametrically contractive mappings." Bulletin of the Australian Mathematical Society 70, no. 3 (December 2004): 463–68. http://dx.doi.org/10.1017/s0004972700034705.

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A contractive mapping on a complete metric space may fail to have a fixed point. Diametrically contractive mappings are introduced and it is shown that a diametrically contractive self-mapping of a weakly compact subset of a Banach space always has a fixed point.

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13

Shukla, Rahul, and Rekha Panicker. "Generalized Enriched Nonexpansive Mappings and Their Fixed Point Theorems." Abstract and Applied Analysis 2023 (December 2, 2023): 1–10. http://dx.doi.org/10.1155/2023/5572893.

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This paper introduces a novel category of nonlinear mappings and provides several theorems on their existence and convergence in Banach spaces, subject to various assumptions. Moreover, we obtain convergence theorems concerning iterates of α -Krasnosel’skiĭ mapping associated with the newly defined class of mappings. Further, we present that α -Krasnosel’skiĭ mapping associated with b -enriched quasinonexpansive mapping is asymptotically regular. Furthermore, some new convergence theorems concerning b -enriched quasinonexpansive mappings have been proved.

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14

Liu, Zhihong, and Saminathan Ponnusamy. "Some properties of univalent log-harmonic mappings." Filomat 32, no. 15 (2018): 5275–88. http://dx.doi.org/10.2298/fil1815275l.

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We determine the representation theorem, distortion theorem, coefficients estimate and Bohr?s radius for log-harmonic starlike mappings of order ?, which are generalization of some earlier results. In addition, the inner mapping radius of log-harmonic mappings is also established by constructing a family of 1-slit log-harmonic mappings. Finally, we introduce pre-Schwarzian, Schwarzian derivatives and Bloch?s norm for non-vanishing log-harmonic mappings, several properties related to these are also obtained.

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15

Chudá, Hana, Nadezda Guseva, and Patrik Peska. "On Fε2-planar mappings with function ε of (pseudo-)Riemannian manifolds." Filomat 31, no. 9 (2017): 2683–89. http://dx.doi.org/10.2298/fil1709683c.

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In this paper we study special mappings between n-dimensional (pseudo-) Riemannian manifolds. In 2003 Topalov introduced PQ?-projectivity of Riemannian metrics, with constant ? ? 0,1 + n. These mappings were studied later by Matveev and Rosemann and they found that for ? = 0 they are projective. These mappings could be generalized for case, when ? will be a function on manifold. We show that PQ?- projective equivalence with ? is a function corresponds to a special case of F-planar mapping, studied by Mikes and Sinyukov (1983) with F = Q. Moreover, the tensor P is derived from the tensor Q and non-zero function ?. We assume that studied mappings will be also F2-planar (Mikes 1994). This is the reason, why we suggest to rename PQ? mapping as F?2. For these mappings we find the fundamental partial differential equations in closed linear Cauchy type form and we obtain new results for initial conditions.

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16

Gupta, Sanjeev, and Laxmi Rathour. "Approximating solutions of general class of variational inclusions involving generalized αiβj-(Hp,φ)-η-accretive mappings." Filomat 37, no. 19 (2023): 6255–75. http://dx.doi.org/10.2298/fil2319255g.

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The present research is an attempt to define a class of generalized ?i?j-(Hp,?)-?-accretive mappings as well as it is a study of its associated class of proximal-point mappings. The generalized ?i?j-(Hp,?)-?-accretive mappings is the sum of two symmetric accretive mappings and an extension of the generalized ??-H(.,.)-accretive mapping [28]. Further the research is a discussion on graph convergence of generalized ?i?j-(Hp,?)-?-accretive mappings and its application includes a set-valued variational-like inclusion problem (SVLIP, in short) in semi inner product spaces. Furthermore an iterative algorithm is proposed, and an attempt is made to discuss the convergence analysis of the sequences generated from the proposed iterative algorithm. An example is constructed that demonstrate few graphics for the convergence of proximal-point mapping. Our results can be viewed as a refinement and generalization of some known results in the literature.

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17

Mohsin, E. A., and Y. Y. Yousif. "Nano perfect mappings." Journal of Interdisciplinary Mathematics 26, no. 7 (2023): 1431–37. http://dx.doi.org/10.47974/jim-1561.

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In this paper, we will introduce and study the concept of nano perfect mappings by using the definition of nano continuous mapping and nano closed mapping, study the relationship between them, and discuss them with many related theories and results. The k-space and its relationship with nano-perfect mapping are also defined.

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18

Mikes, Josef, and Lenka Rýparová. "Rotary mappings of spaces with affine connection." Filomat 33, no. 4 (2019): 1147–52. http://dx.doi.org/10.2298/fil1904147m.

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This paper concerns with rotary mappings of two-dimensional spaces with an affine connection onto (pseudo-) Riemannian spaces. The results obtained in the theory of rotary mappings are further developed. We prove that any (pseudo-) Riemannian space admits rotary mapping. There are also presented certain properties from which yields the existence of these rotary mappings.

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19

Poliquin, R. A. "A Characterization of Proximal Subgradient Set-Valued Mappings." Canadian Mathematical Bulletin 36, no. 1 (March 1, 1993): 116–22. http://dx.doi.org/10.4153/cmb-1993-017-4.

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AbstractIn this paper we tackle the problem of identifying set-valued mappings that are subgradient set-valued mappings. We show that a set-valued mapping is the proximal subgradient mapping of a lower semicontinuous function bounded below by a quadratic if and only if it satisfies a monotone selection property.

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20

KHAMSI, M. A., and A. R. KHAN. "Goebel and Kirk fixed point theorem for multivalued asymptotically nonexpansive mappings." Carpathian Journal of Mathematics 33, no. 3 (2017): 335–42. http://dx.doi.org/10.37193/cjm.2017.03.08.

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We introduce the concept of a multivalued asymptotically nonexpansive mapping and establish Goebel and Kirk fixed point theorem for these mappings in uniformly hyperbolic metric spaces. We also define a modified Mann iteration process for this class of mappings and obtain an extension of some well-known results for singlevalued mappings defined on linear as well as nonlinear domains.

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21

Charatonik, J. J. "Mappings Confluent over Locally Connected Continua." gmj 11, no. 4 (December 2004): 671–80. http://dx.doi.org/10.1515/gmj.2004.671.

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Abstract A mapping is said to be confluent over locally connected continua if for each locally connected subcontinuum 𝑄 of the range each component of its preimage is mapped onto 𝑄. For mappings of compact spaces this class is a very natural generalization of locally confluent mappings. Various properties of these mappings are systematically studied in the paper.

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22

Swaminathan, A., and Sankari M. "Somewhat precontinuous mappings via grill." Boletim da Sociedade Paranaense de Matemática 41 (December 24, 2022): 1–5. http://dx.doi.org/10.5269/bspm.51504.

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This article introduces the concepts of somewhat G-precontinuous mapping and somewhat G-preopen mappings. Using these notions, some examples and few interesting properties of those mappings are discussed by means of grill topological spaces.

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23

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."

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24

Plewik, Szymon. "On closed mappings." Czechoslovak Mathematical Journal 38, no. 2 (1988): 313–18. http://dx.doi.org/10.21136/cmj.1988.102226.

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25

Schutz, John W. "The isotropy mappings of Minkowski space-time generate the orthochronous poincaré group." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 31, no. 4 (April 1990): 425–33. http://dx.doi.org/10.1017/s0334270000006767.

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AbstractMinkowski space-time is specified with respect to a single coordinate frame by the set of timelike lines. Isotropy mappings are defined as automorphisms which leave the events of one timelike line invariant. We demonstrate the existence of two special types of isotropy mappings. The first type of isotropy mapping induce orthogonal transformations in position space. Mappings of the second type can be composed to generate Lorentz boosts. It is shown that isotropy mappings generate the orthochronous Poincaré group of motions. The set of isotropy mappings then maps the single assumed coordinate frame onto a set of coordinate frames related by transformations of the orthochronous Poincaré group.

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26

Najdanovic, Marija, Milan Zlatanovic, and Irena Hinterleitner. "Conformal and geodesic mappings of generalized equidistant spaces." Publications de l'Institut Math?matique (Belgrade) 98, no. 112 (2015): 71–84. http://dx.doi.org/10.2298/pim1512071n.

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We consider conformal and geodesic mappings of generalized equidistant spaces. We prove the existence of mentioned nontrivial mappings and construct examples of conformal and geodesic mapping of a 3-dimensional generalized equidistant space. Also, we find some invariant objects (three tensors and four which are not tensors) of special geodesic mapping of generalized equidistant space.

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27

Kaur, Sandeep, and Alkan Özkan. "Some results on soft equicontinuity and soft uniform equicontinuity." Filomat 35, no. 12 (2021): 4095–103. http://dx.doi.org/10.2298/fil2112095k.

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Equicontinuity plays a vital role in general metric spaces and multiple studies have tried to characterize equicontinuity since its origin. Advent of soft set theory leads us to study these mappings in terms of soft sets, as well. In this paper, first we introduce the concept of soft equicontinuity, soft pointwise equicontinuity and soft uniform equicontinuity with examples. Moreover, we explore soft continuity of soft pointwise limit of a sequence of soft mappings when the family of the given soft mapping is a soft equicontinuous mapping and then discuss soft pointwise convergence of sequence of soft mappings which are a soft pointwise equicontinuous mappings when co-domain is soft complete space. We also give characterizations of soft pointwise equicontinuity and soft uniform equicontinuity in terms of convergent sequence of soft points in soft dense subset.

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28

Liu, Peide, Muhammad Bilal Khan, Muhammad Aslam Noor, and Khalida Inayat Noor. "On Strongly Generalized Preinvex Fuzzy Mappings." Journal of Mathematics 2021 (April 1, 2021): 1–16. http://dx.doi.org/10.1155/2021/6657602.

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In this article, we introduce a new notion of generalized convex fuzzy mapping known as strongly generalized preinvex fuzzy mapping on the invex set. Firstly, we have investigated some properties of strongly generalized preinvex fuzzy mapping. In particular, we establish the equivalence among the strongly generalized preinvex fuzzy mapping, strongly generalized invex fuzzy mapping, and strongly generalized monotonicity. We also prove that the optimality conditions for the sum of G-differentiable preinvex fuzzy mappings and non-G-differentiable strongly generalized preinvex fuzzy mappings can be characterized by strongly generalized fuzzy mixed variational-like inequalities, which can be viewed as a novel and innovative application. Several special cases are discussed. Results obtained in this paper can be viewed as improvement and refinement of previously known results.

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29

MOSLEHIAN, MOHAMMAD SAL, ALI ZAMANI, and PAWEŁ WÓJCIK. "APPROXIMATELY ANGLE PRESERVING MAPPINGS." Bulletin of the Australian Mathematical Society 99, no. 03 (February 14, 2019): 485–96. http://dx.doi.org/10.1017/s0004972718001430.

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We study linear mappings which preserve vectors at a specific angle. We introduce the concept of $(\unicode[STIX]{x1D700},c)$ -angle preserving mappings and define $\widehat{\unicode[STIX]{x1D700}}\,(T,c)$ as the ‘smallest’ number $\unicode[STIX]{x1D700}$ for which $T$ is an $(\unicode[STIX]{x1D700},c)$ -angle preserving mapping. We derive an exact formula for $\widehat{\unicode[STIX]{x1D700}}\,(T,c)$ in terms of the norm $\Vert T\Vert$ and the minimum modulus $[T]$ of $T$ . Finally, we characterise approximately angle preserving mappings.

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30

De la Sen, Manuel, and Asier Ibeas. "Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/948749.

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This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

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31

Cichoń, J., J. D. Mitchell, and M. Morayne. "Generating continuous mappings with Lipschitz mappings." Transactions of the American Mathematical Society 359, no. 5 (December 15, 2006): 2059–74. http://dx.doi.org/10.1090/s0002-9947-06-04026-8.

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32

Bresar, Matej. "Commuting Traces of Biadditive Mappings, Commutativity-Preserving Mappings and Lie Mappings." Transactions of the American Mathematical Society 335, no. 2 (February 1993): 525. http://dx.doi.org/10.2307/2154392.

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33

Jain, Kapil, Jatinderdeep Kaur, and Satvinder Singh Bhatia. "Fixed Points of \(\xi\) - (\(\alpha\), \(\beta\))- Contractive Mappings in b-Metric Spaces." Journal of Advances in Mathematics and Computer Science 38, no. 6 (March 22, 2023): 6–15. http://dx.doi.org/10.9734/jamcs/2023/v38i61764.

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In the paper [Some new observations on Geraghty and \(\acute{C}\)iri\(\acute{c}\) type results in b-metric spaces, Mathematics, 7, (2019), doi: 10.3390/math7070643] Mlaiki et al. introduced (\(\alpha\), \(\beta\))-type contraction in order to generalize the contraction mapping defined by Pant and Panicker. Also, in the paper [Some fixed point results in b- metric spaces and b-metric-like spaces with new contractive mappings, Axioms, 10(2), (2021), 15 pages, doi: 10.3390/axioms10020055] Jain and Kaur presented the concepts of \(\xi\) -contractive mappings. Now, the aim of the present article is to introduce \(\xi\) - (\(\alpha\), \(\beta\)) -contractive mappings in b-metric spaces by combining the concepts (\(\alpha\), \(\beta\))-type contraction and \(\xi\)-contractive mappings. Also, we establish some fixed point results for newly defined mappings. Our results generalize various theorems in literature. In support, we provide an example.

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34

Basalaev, S. G. "Усреднения компактных отображений группы Энгеля." Владикавказский математический журнал, no. 1 (March 23, 2023): 5–19. http://dx.doi.org/10.46698/n0927-3994-6949-u.

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The contact mappings belonging to the metric Sobolev classes are studied on an Engel group with a left-invariant sub-Riemannian metric. In the Euclidean space one of the main methods to handle non-smooth mappings is the mollification, i.e., the convolution with a smooth kernel. An extra difficulty arising with contact mappings of Carnot groups is that the mollification of a contact mapping is usually not contact. Nevertheless, in the case considered it is possible to estimate the magnitude of deviation of contactness sufficiently to obtain useful results. We obtain estimates on convergence (or sometimes divergence) of the components of the differential of the mollified mapping to the corresponding components of the Pansu differential of the contact mapping. As an application to the quasiconformal analysis, we present alternative proofs of the convergence of mollified horizontal exterior forms and the commutativity of the pull-back of the exterior form by the Pansu differential with the exterior differential in the weak sense. These results in turn allow us to obtain such basic properties of mappings with bounded distortion as H\"older continuity, differentiability almost everywhere in the sense of Pansu, Luzin $\mathcal{N}$-property.

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35

Kangtunyakarn, Atid, and Sarawut Suwannaut. "The Iterative Method for Generalized Equilibrium Problems and a Finite Family of Lipschitzian Mappings in Hilbert Spaces." Journal of Mathematics 2022 (May 12, 2022): 1–23. http://dx.doi.org/10.1155/2022/8686041.

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In this research, we introduced the S -mapping generated by a finite family of contractive mappings, Lipschitzian mappings and finite real numbers using the results of Kangtunyakarn (2013). Then, we prove the strong convergence theorem for fixed point sets of finite family of contraction and Lipschitzian mapping and solution sets of the modified generalized equilibrium problem introduced by Suwannaut and Kangtunyakarn (2014). Finally, numerical examples are provided to illustrate our main theorem.

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36

Kutbi, Marwan Amin, and Wutiphol Sintunavarat. "On the Solution Existence of Variational-Like Inequalities Problems for Weakly Relaxedη−αMonotone Mapping." Abstract and Applied Analysis 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/207845.

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We introduce two new concepts of weakly relaxedη-αmonotone mappings and weakly relaxedη-αsemimonotone mappings. Using the KKM technique, the existence of solutions for variational-like problems with weakly relaxedη-αmonotone mapping in reflexive Banach spaces is established. Also, we obtain the existence of solution for variational-like problems with weakly relaxedη-αsemimonotone mappings in arbitrary Banach spaces by using the Kakutani-Fan-Glicksberg fixed-point theorem.

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37

Shi, Qingtian. "Equivalent characterizations of harmonic Teichmüller mappings." AIMS Mathematics 7, no. 6 (2022): 11015–23. http://dx.doi.org/10.3934/math.2022615.

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<abstract><p>In this paper, three equivalent conditions of $ \rho $-harmonic Teichmüller mapping are given firstly. As an application, we investigate the relationship between a $ \rho $-harmonic Teichmüller mapping and its associated holomorphic quadratic differential and obtain a relatively simple method to prove Theorem 2.1 in <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. Furthermore, the representation theorem of $ 1/|\omega|^{2} $-harmonic Teichmüller mappings is given as a by-product. Our results extend the corresponding researches of harmonic Teichmüller mappings.</p></abstract>

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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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Shioji, Naoki, Tomonari Suzuki, and Wataru Takahashi. "Contractive mappings, Kannan mappings and metric completeness." Proceedings of the American Mathematical Society 126, no. 10 (1998): 3117–24. http://dx.doi.org/10.1090/s0002-9939-98-04605-x.

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40

Stankovic, Mica, Marija Ciric, and Milan Zlatanovic. "Geodesic mappings of equiaffine and anti-equiaffine general affine connection spaces preserving torsion." Filomat 26, no. 3 (2012): 439–51. http://dx.doi.org/10.2298/fil1203439s.

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In this paper we consider equitorsion geodesic mappings of equiaffine spaces of the ?-kind, ? ? {0, ..., 5}. In the case when ? ? {0, 5}, vector ?i , which determines that mapping, is gradient, which doesn?t hold in general case. We found the condition when the vector ?i is gradient in the case of ? ? {1, ..., 4}. Some invariant geometric objects of such mappings are found. Anti-equiaffine spaces of ?-kind, ? ? {0, ..., 5} are introduced and discussed. Equitorsion geodesic mappings of such spaces are described and some invariants are found.

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Albişoru, Andrei-Florin, and Dorin Ghişa. "Conformal Self Mappings of the Fundamental Domains of Analytic Functions and Computer Experimentation." WSEAS TRANSACTIONS ON MATHEMATICS 22 (September 26, 2023): 652–65. http://dx.doi.org/10.37394/23206.2023.22.72.

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Conformal self mappings of a given domain of the complex plane can be obtained by using the Riemann Mapping Theorem in the following way. Two different conformal mappings φ and ψ of that domain onto one of the standard domains: the unit disc, the complex plane or the Riemann sphere are taken and then ψ −1 ◦ φ is what we are looking for. Yet, this is just a theoretical construction, since the Riemann Mapping Theorem does not offer any concrete expression of those functions. The Möbius transformations are concrete, but they can be used only for particular circular domains. We are proving in this paper that conformal self mappings of any fundamental domain of an arbitrary analytic function can be obtained via Möbius transformations as long as we allow that domain to have slits. Moreover, those mappings enjoy group properties. This is a totally new topic. Although fundamental domains of some elementary functions are well known, the existence of such domains for arbitrary analytic functions has been proved only in our previous publications mentioned in the References section. No other publication exists on this topic and the reference list is complete. We deal here with conformal self mappings of fundamental domains in its whole generality and present sustaining illustrations. Those related to the case of Dirichlet functions represent a real achievement. Computer experimentation with these mappings are made for the most familiar analytic functions.

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Salisu, Sani, Vasile Berinde, Songpon Sriwongsa, and Poom Kumam. "Approximating fixed points of demicontractive mappings in metric spaces by geodesic averaged perturbation techniques." AIMS Mathematics 8, no. 12 (2023): 28582–600. http://dx.doi.org/10.3934/math.20231463.

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<abstract><p>In this article, we introduce the fundamentals of the theory of demicontractive mappings in metric spaces and expose the key concepts and tools for building a constructive approach to approximating the fixed points of demicontractive mappings in this setting. By using an appropriate geodesic averaged perturbation technique, we obtained strong convergence and $ \Delta $-convergence theorems for a Krasnoselskij-Mann type iterative algorithm to approximate the fixed points of quasi-nonexpansive mappings within the framework of CAT(0) spaces. The main results obtained in this nonlinear setting are natural extensions of the classical results from linear settings (Hilbert and Banach spaces) for both quasi-nonexpansive mappings and demicontractive mappings. We applied our results to solving an equilibrium problem in CAT(0) spaces and showed how we can approximate the equilibrium points by using our fixed point results. In this context we also provided a numerical example in the case of a demicontractive mapping that is not a quasi-nonexpansive mapping and highlighted the convergence pattern of the algorithm in <xref ref-type="table" rid="Table1">Table 1</xref>. It is important to note that the numerical example is set in non-Hilbert CAT(0) spaces.</p> </abstract>

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43

Thakur, S. S., and R. Malviya. "Pairwise fuzzy irresolute mappings." Mathematica Bohemica 121, no. 3 (1996): 273–80. http://dx.doi.org/10.21136/mb.1996.125992.

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Turcanu, Teodor, and Mihai Postolache. "On Enriched Suzuki Mappings in Hadamard Spaces." Mathematics 12, no. 1 (January 3, 2024): 157. http://dx.doi.org/10.3390/math12010157.

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We define and study enriched Suzuki mappings in Hadamard spaces. The results obtained here are extending fundamental findings previously established in related research. The extension is realized with respect to at least two different aspects: the setting and the class of involved operators. More accurately, Hilbert spaces are particular Hadamard spaces, while enriched Suzuki nonexpansive mappings are natural generalizations of enriched nonexpansive mappings. Next, enriched Suzuki nonexpansive mappings naturally contain Suzuki nonexpansive mappings in Hadamard spaces. Besides technical lemmas, the results of this paper deal with (1) the existence of fixed points for enriched Suzuki nonexpansive mappings and (2) Δ and strong (metric) convergence of Picard iterates of the α-averaged mapping, which are exactly Krasnoselskij iterates for the original mapping.

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Bshouty, D., W. Hengartner, and O. Hossian. "Harmonic typically real mappings." Mathematical Proceedings of the Cambridge Philosophical Society 119, no. 4 (May 1996): 673–80. http://dx.doi.org/10.1017/s030500410007451x.

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AbstractWe give an example of a univalent orientation-preserving harmonic mapping f = h + g¯ defined on the unit disc U which is real on the real axis, satisfies and is not typically real. Furthermore, we give a geometric characterization for univalent, harmonic and typically real mappings.

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Vesic, Nenad. "Some invariants of conformal mappings of a generalized Riemannian space." Filomat 32, no. 4 (2018): 1465–74. http://dx.doi.org/10.2298/fil1804465v.

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Invariants of conformal mappings between non-symmetric affine connection spaces are obtained in this paper. Correlations between these invariants and the Weyl conformal curvature tensor are established. Before these invariants, it is obtained a necessary and sufficient condition for a mapping to be conformal. Some appurtenant invariants of conformal mappings are obtained.

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Reich, Edgar. "Harmonic mappings and ouasiconformal mappings." Journal d'Analyse Mathématique 46, no. 1 (December 1986): 239–45. http://dx.doi.org/10.1007/bf02796588.

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Saluja, Gurucharan, and Mihai Postolache. "Three-step iterations for total asymptotically nonexpansive mappings in CAT(0) spaces." Filomat 31, no. 5 (2017): 1317–30. http://dx.doi.org/10.2298/fil1705317s.

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In this paper, we establish strong and ?-convergence theorems of modified three-step iterations for total asymptotically nonexpansive mapping which is wider than the class asymptotically nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and generalize the corresponding results of Chang et al. [Demiclosed principle and ?-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Appl. Math. Comput. 219(5) (2012) 2611-2617], Nanjaras and Panyanak [Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. Vol. 2010, Art. ID 268780], and many others.

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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.

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CHEN, XINGDI, and YUQIN QUE. "QUASICONFORMAL EXTENSIONS OF HARMONIC MAPPINGS WITH A COMPLEX PARAMETER." Journal of the Australian Mathematical Society 102, no. 3 (September 19, 2016): 307–15. http://dx.doi.org/10.1017/s1446788716000355.

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In this paper, we study quasiconformal extensions of harmonic mappings. Utilizing a complex parameter, we build a bridge between the quasiconformal extension theorem for locally analytic functions given by Ahlfors [‘Sufficient conditions for quasiconformal extension’, Ann. of Math. Stud.79 (1974), 23–29] and the one for harmonic mappings recently given by Hernández and Martín [‘Quasiconformal extension of harmonic mappings in the plane’, Ann. Acad. Sci. Fenn. Math.38 (2) (2013), 617–630]. We also give a quasiconformal extension of a harmonic Teichmüller mapping, whose maximal dilatation estimate is asymptotically sharp.

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