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Journal articles on the topic 'Mappings (Mathematics); Fixed point theory; Convex domains'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

Ahmad, Junaid, Kifayat Ullah, Hüseyin Işik, Muhammad Arshad, and Manuel de la Sen. "Iterative Construction of Fixed Points for Operators Endowed with Condition E in Metric Spaces." Advances in Mathematical Physics 2021 (July 9, 2021): 1–8. http://dx.doi.org/10.1155/2021/7930128.

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We consider the class of mappings endowed with the condition E in a nonlinear domain called 2-uniformly convex hyperbolic space. We provide some strong and Δ -convergence theorems for this class of mappings under the Agarwal iterative process. In order to support the main outcome, we procure an example of mappings endowed with the condition E and prove that its Agarwal iterative process is more effective than Mann and Ishikawa iterative processes. Simultaneously, our results hold in uniformly convex Banach, CAT(0), and some CAT( κ ) spaces. This approach essentially provides a new setting for researchers who are working on the iterative procedures in fixed point theory and applications.

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2

Muhammad, Noor, Ali Asghar, Samina Irum, Ali Akgül, E. M. Khalil, and Mustafa Inc. "Approximation of fixed point of generalized non-expansive mapping via new faster iterative scheme in metric domain." AIMS Mathematics 8, no. 2 (2022): 2856–70. http://dx.doi.org/10.3934/math.2023149.

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<abstract><p>In this paper, we establish a new iterative process for approximation of fixed points for contraction mappings in closed, convex metric space. We conclude that our iterative method is more accurate and has very fast results from previous remarkable iteration methods like Picard-S, Thakur new, Vatan Two-step and K-iterative process for contraction. Stability of our iteration method and data dependent results for contraction mappings are exact, correspondingly on testing our iterative method is advanced. Finally, we prove enquiring results for some weak and strong convergence theorems of a sequence which is generated from a new iterative method, Suzuki generalized non-expansive mappings with condition $ (C) $ in uniform convexity of metric space. Our results are addition, enlargement over and above generalization for some well-known conclusions with literature for theory of fixed point.</p></abstract>

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3

Abu-Muhanna, Yusuf, and Glenn Schober. "Harmonic Mappings onto Convex Domains." Canadian Journal of Mathematics 39, no. 6 (December 1, 1987): 1489–530. http://dx.doi.org/10.4153/cjm-1987-071-4.

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Let D be a simply-connected domain and w0 a fixed point of D. Denote by SD the set of all complex-valued, harmonic, orientation-preserving, univalent functions f from the open unit disk U onto D with f(0) = w0. Unlike conformai mappings, harmonic mappings are not essentially determined by their image domains. So, it is natural to study the set SD.In Section 2, we give some mapping theorems. We prove the existence, when D is convex and unbounded, of a univalent, harmonic solution f of the differential equationwhere a is analytic and |a| < 1, such that f(U) ⊂ D and

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4

Khan, Safeer Hussain. "Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain." Abstract and Applied Analysis 2014 (2014): 1–5. http://dx.doi.org/10.1155/2014/401650.

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We use a three-step iterative process to prove some strong andΔ-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains) as well as CAT(0) spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0) spaces.

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5

MURESAN, VIORICA, and ANTON S. MURESAN. "On the theory of fixed point theorems for convex contraction mappings." Carpathian Journal of Mathematics 31, no. 3 (2015): 365–71. http://dx.doi.org/10.37193/cjm.2015.03.13.

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Based on the concepts and problems introduced in [Rus, I. A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541–559], in the present paper we consider the theory of some fixed point theorems for convex contraction mappings. We give some results on the following aspects: data dependence of fixed points; sequences of operators and fixed points; well-posedness of a fixed point problem; limit shadowing property and Ulam-Hyers stability for fixed point equations.

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6

MURESAN, ANTON S. "The theory of some asymptotic fixed point theorems." Carpathian Journal of Mathematics 30, no. 3 (2014): 361–68. http://dx.doi.org/10.37193/cjm.2014.03.07.

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In this paper we present the theory about some fixed point theorems for convex contraction mappings. We give some results on data dependence of fixed points, on sequences of operators and fixed points, on well-possedness of fixed point problem, on limit shadowing property and on Ulam-Hyers stability for equations of fixed points.

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7

FUKHAR-UD-DIN, HAFIZ. "Existence and approximation of a fixed point of a fundamentally nonexpansive mapping in hyperbolic spaces." Carpathian Journal of Mathematics 36, no. 1 (March 1, 2020): 71–80. http://dx.doi.org/10.37193/cjm.2020.01.07.

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We prove that a fundamentally nonexpansive mapping on a compact and convex subset of a hyperbolic space, has a fixed point. We also show that one-step iterative algorithm of two mappings is vital for the approximation of a common fixed point of two fundamentally nonexpansive mappings in a strictly convex hyperbolic space. Our results are new in metric fixed point theory and generalize several existing results.

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8

ALTUN, ISHAK, and GULHAN MINAK. "An extension of Assad-Kirk’s fixed point theorem for multivalued nonself mappings." Carpathian Journal of Mathematics 32, no. 2 (2016): 147–55. http://dx.doi.org/10.37193/cjm.2016.02.02.

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In the present paper, taking into account the recent developments on the theory of fixed point, we give some fixed point results for multivalued nonself mappings on complete metrically convex metric spaces. Our main result properly includes the famous Assad-Kirk fixed point theorem for nonself mappings. Also, we provide a nontrivial example which shows the motivation for such investigations of multivalued nonself contraction mappings.

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9

MA, TSOY-WO. "INVERSE MAPPING THEOREM ON COORDINATE SPACES." Bulletin of the London Mathematical Society 33, no. 4 (July 2001): 473–82. http://dx.doi.org/10.1017/s0024609301008050.

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A mean-value theorem, an inverse mapping theorem and an implicit mapping theorem are established here in a class of complex locally convex spaces, including the spaces of test functions in distribution theory. Our main tool is the integral formula and the invariance of the domain, derived from topological degrees, rather than from fixed points of contractions in Banach spaces.

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10

O'Regan, Donal. "Coincidence Principles and Fixed Point Theory for Mappings in Locally Convex Spaces." Rocky Mountain Journal of Mathematics 28, no. 4 (December 1998): 1407–45. http://dx.doi.org/10.1216/rmjm/1181071724.

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11

Atsushiba, Sachiko, and Wataru Takahashi. "Approximating common fixed points of two nonexpansive mappings in Banach spaces." Bulletin of the Australian Mathematical Society 57, no. 1 (February 1998): 117–27. http://dx.doi.org/10.1017/s0004972700031464.

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Let C be a nonempty closed convex subset of a real Banach space E and let S, T be nonexpansive mappings of C into itself. In this paper, we consider the following iteration procedure of Mann's type for approximating common fixed points of two mappings S and T:where {αn is a sequence in [0,1]. Using some ideas in the nonlinear ergodic theory, we prove that the iterates converge weakly to a common fixed point of the nonexpansive mappings T and S in a uniformly convex Banach space which satisfies Opial's condition or whose norm is Fréchet differentiable.

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12

Ben Amar, Afif, Mohamed Amine Cherif, and Maher Mnif. "Fixed-Point Theory on a Frechet Topological Vector Space." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–9. http://dx.doi.org/10.1155/2011/390720.

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We establish some versions of fixed-point theorem in a Frechet topological vector spaceE. The main result is that every mapA=BC(whereBis a continuous map andCis a continuous linear weakly compact operator) from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point. Based on this result, we present two versions of the Krasnoselskii fixed-point theorem. Our first result extend the well-known Krasnoselskii's fixed-point theorem forU-contractions and weakly compact mappings, while the second one, by assuming that the family{T(⋅,y):y∈C(M)whereM⊂EandC:M→Ea compactoperator}is nonlinearφequicontractive, we give a fixed-point theorem for the operator of the formEx:=T(x,C(x)).

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13

Lu, Haishu, Kai Zhang, and Rong Li. "Collectively fixed point theorems in noncompact abstract convex spaces with applications." AIMS Mathematics 6, no. 11 (2021): 12422–59. http://dx.doi.org/10.3934/math.2021718.

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<abstract><p>In this paper, by using the KKM theory and the properties of $ \Gamma $-convexity and $ {\frak{RC}} $-mapping, we investigate the existence of collectively fixed points for a family with a finite number of set-valued mappings on the product space of noncompact abstract convex spaces. Consequently, as applications, some existence theorems of generalized weighted Nash equilibria and generalized Pareto Nash equilibria for constrained multiobjective games, some nonempty intersection theorems with applications to the Fan analytic alternative formulation and the existence of Nash equilibria, and some existence theorems of solutions for generalized weak implicit inclusion problems in noncompact abstract convex spaces are given. The results obtained in this paper extend and generalize many corresponding results of the existing literature.</p></abstract>

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14

Choudhury, Masudul Alam. "On the Existence of Evolutionary Learning Equilibriums." Sultan Qaboos University Journal for Science [SQUJS] 16 (December 1, 2011): 68. http://dx.doi.org/10.24200/squjs.vol16iss0pp68-81.

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The usual kinds of Fixed-Point Theorems formalized on the existence of competitive equilibrium that explain much of economic theory at the core of economics can operate only on bounded and closed sets with convex mappings. But these conditions are hardly true of the real world of economic and financial complexities and perturbations. The category of learning sets explained by continuous fields of interactive, integrative and evolutionary behaviour caused by dynamic preferences at the individual and institutional and social levels cannot maintain the assumption of closed, bounded and convex sets. Thus learning sets and multi-system inter-temporal relations explained by pervasive complementarities and participation between variables and entities, and evolution by learning, have evolutionary equilibriums. Such a study requires a new methodological approach. This paper formalizes such a methodology for evolutionary equilibriums in learning spaces. It briefly points out the universality of learning equilibriums in all mathematical structures. For a particular case though, the inter-systemic interdependence between sustainable development and ethics and economics in the specific understanding of learning domain is pointed out.

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15

Ullah, Kifayat, and Muhammad Arshad. "Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process." Filomat 32, no. 1 (2018): 187–96. http://dx.doi.org/10.2298/fil1801187u.

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In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of uniformly convex Banach spaces. Numerical example is given to show the efficiency of new iteration process. Our results are the extension, improvement and generalization of many known results in the literature of iterations in fixed point theory.

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16

Thianwan, Tanakit. "Mixed Type Algorithms for Asymptotically Nonexpansive Mappings in Hyperbolic Spaces." European Journal of Pure and Applied Mathematics 14, no. 3 (August 5, 2021): 650–65. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.4005.

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In this paper, a new mixed type iteration process for approximating a common fixed point of two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings is constructed. We then establish a strong convergence theorem under mild conditions in a uniformly convex hyperbolic space. The results presented here extend and improve some related results in the literature.

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17

Aron, David, and Santosh Kumar. "Fixed point theorem for a sequence of multivalued nonself mappings in metrically convex metric spaces." Topological Algebra and its Applications 10, no. 1 (January 1, 2022): 1–12. http://dx.doi.org/10.1515/taa-2020-0108.

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Abstract In this paper, a common fixed point theorem is demonstrated for a sequence of multivalued mappings which satisfy certain requirements in complete metric spaces. The results proved here will generalize and extend the results due to Ćirić [1]. Suitable examples are given at the end to support the results proved herein.

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18

Shukla, Rahul, Rajendra Pant, and Winter Sinkala. "A General Picard-Mann Iterative Method for Approximating Fixed Points of Nonexpansive Mappings with Applications." Symmetry 14, no. 8 (August 21, 2022): 1741. http://dx.doi.org/10.3390/sym14081741.

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Fixed point theory provides an important structure for the study of symmetry in mathematics. In this article, a new iterative method (general Picard–Mann) to approximate fixed points of nonexpansive mappings is introduced and studied. We study the stability of this newly established method which we find to be summably almost stable for contractive mappings. A number of weak and strong convergence theorems of such iterative methods are established in the setting of Banach spaces under certain geometrical assumptions. Finally, we present a number of applications to address various important problems (zero of an accretive operator, mixed equilibrium problem, convex optimization problem, split feasibility problem, periodic solution of a nonlinear evolution equation) appearing in the field of nonlinear analysis.

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19

Jaradat, Mohammed M. M., Babak Mohammadi, Vahid Parvaneh, Hassen Aydi, and Zead Mustafa. "PPF-Dependent Fixed Point Results for Multi-Valued ϕ-F-Contractions in Banach Spaces and Applications." Symmetry 11, no. 11 (November 6, 2019): 1375. http://dx.doi.org/10.3390/sym11111375.

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The solutions for many real life problems is obtained by interpreting the given problem mathematically in the form of f ( x ) = x . One of such examples is that of the famous Borsuk–Ulam theorem, in which using some fixed point argument, it can be guaranteed that at any given time we can find two diametrically opposite places in a planet with same temperature. Thus, the correlation of symmetry is inherent in the study of fixed point theory. In this paper, we initiate ϕ − F -contractions and study the existence of PPF-dependent fixed points (fixed points for mappings having variant domains and ranges) for these related mappings in the Razumikhin class. Our theorems extend and improve the results of Hammad and De La Sen [Mathematics, 2019, 7, 52]. As applications of our PPF dependent fixed point results, we study the existence of solutions for delay differential equations (DDEs) which have numerous applications in population dynamics, bioscience problems and control engineering.

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20

Chuadchawna, Preeyalak, Ali Farajzadeh, and Anchalee Kaewcharoen. "Convergence theorems for total asymptotically nonexpansive single-valued and quasi nonexpansive multi-valued mappings in hyperbolic spaces." Journal of Applied Analysis 27, no. 1 (December 24, 2020): 129–42. http://dx.doi.org/10.1515/jaa-2020-2038.

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Abstract In this paper, we discuss the Δ-convergence and strong convergence for the iterative sequence generated by the proposed scheme to approximate a common fixed point of a total asymptotically nonexpansive single-valued mapping and a quasi nonexpansive multi-valued mapping in a complete uniformly convex hyperbolic space. Finally, by giving an example, we illustrate our result.

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21

Sahoo, Soubhagya Kumar, Muhammad Tariq, Hijaz Ahmad, Ayman A. Aly, Bassem F. Felemban, and Phatiphat Thounthong. "Some Hermite–Hadamard-Type Fractional Integral Inequalities Involving Twice-Differentiable Mappings." Symmetry 13, no. 11 (November 19, 2021): 2209. http://dx.doi.org/10.3390/sym13112209.

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The theory of fractional analysis has been a focal point of fascination for scientists in mathematical science, given its essential definitions, properties, and applications in handling real-life problems. In the last few decades, many mathematicians have shown their considerable interest in the theory of fractional calculus and convexity due to their wide range of applications in almost all branches of applied sciences, especially in numerical analysis, physics, and engineering. The objective of this article is to establish Hermite-Hadamard type integral inequalities by employing the k-Riemann-Liouville fractional operator and its refinements, whose absolute values are twice-differentiable h-convex functions. Moreover, we also present some special cases of our presented results for different types of convexities. Moreover, we also study how q-digamma functions can be applied to address the newly investigated results. Mathematical integral inequalities of this class and the arrangements associated have applications in diverse domains in which symmetry presents a salient role.

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22

Abass, H. A., L. O. Jolaoso, and O. T. Mewomo. "Convergence analysis for split hierachical monotone variational inclusion problem in Hilbert spaces." Topological Algebra and its Applications 10, no. 1 (January 1, 2022): 167–84. http://dx.doi.org/10.1515/taa-2022-0124.

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Abstract In this paper, we introduce a new iterative algorithm for approximating a common solution of Split Hierarchical Monotone Variational Inclusion Problem (SHMVIP) and Fixed Point Problem (FPP) of k-strictly pseudocontractive mappings in real Hilbert spaces. Our proposed method converges strongly, does not require the estimation of operator norm and it is without imposing the strict condition of compactness; these make our method to be potentially more applicable than most existing methods in the literature. Under standard and mild assumption of monotonicity of the SHMVIP associated mappings, we establish the strong convergence of the iterative algorithm.We present some applications of our main result to approximate the solution of Split Hierarchical Convex Minimization Problem (SHCMP) and Split Hierarchical Variational Inequality Problem (SHVIP). Some numerical experiments are presented to illustrate the performance and behavior of our method. The result presented in this paper extends and complements some related results in literature.

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23

Piatek, Bozena. "Iterated nonexpansive mappings in Hilbert spaces." Journal of Fixed Point Theory and Applications 23, no. 4 (September 16, 2021). http://dx.doi.org/10.1007/s11784-021-00898-6.

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AbstractIn [T. Dominguez Benavides and E. Llorens-Fuster, Iterated nonexpansive mappings, J. Fixed Point Theory Appl. 20 (2018), no. 3, Paper No. 104, 18 pp.], the authors raised the question about the existence of a fixed point free continuous INEA mapping T defined on a closed convex and bounded subset (or on a weakly compact convex subset) of a Banach space with normal structure. Our main goal is to give the affirmative answer to this problem in the very special case of a Hilbert space.

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24

Ullah, Kifayat, and Junaid Ahmad. "Some convergence results using K iteration process in Banach Spaces." Asian-European Journal of Mathematics, March 12, 2022. http://dx.doi.org/10.1142/s1793557122502102.

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In this paper, we establish several strong and weak convergence results for a class of mappings which is essentially wider than the class of Suzuki mappings using [Formula: see text] iteration process in the context of uniformly convex Banach spaces. We also provide an example for support of our results. The obtained results are the extension and improvement of some recent results in the fixed point approximations theory.

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25

Izuchukwu, C., F. O. Isiogugu, and C. C. Okeke. "A new viscosity-type iteration for a finite family of split variational inclusion and fixed point problems between Hilbert and Banach spaces." Journal of Inequalities and Applications 2019, no. 1 (September 23, 2019). http://dx.doi.org/10.1186/s13660-019-2201-9.

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Abstract In this paper, we introduce a new viscosity-type iteration process for approximating a common solution of a finite family of split variational inclusion problem and fixed point problem. We prove that the proposed algorithm converges strongly to a common solution of a finite family of split variational inclusion problems and fixed point problem for a finite family of type-one demicontractive mappings between a Hilbert space and a Banach space. Furthermore, we applied our results to study a finite family of split convex minimization problems, and also considered a numerical experiment of our results to further illustrate its applicability. Our results extend and improve the results of Byrne et al. (J. Nonlinear Convex Anal. 13:759–775, 2012), Kazmi and Rizvi (Optim. Lett. 8(3):1113–1124, 2014), Moudafi (J. Optim. Theory Appl. 150:275–283, 2011), Shehu and Ogbuisi (Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 110(2):503–518, 2016), Takahashi and Yao (Fixed Point Theory Appl. 2015:87, 2015), Chidume and Ezeora (Fixed Point Theory Appl. 2014:111, 2014), and a host of other important results in this direction.

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26

Ahmadi, Zahra, Rahmatollah Lashkaripour, and Hamid Baghani. "Fixed point theorems for a new generalization of contractive maps in incomplete metric spaces and its application in boundary value problems." Journal of Applied Analysis, February 2, 2021. http://dx.doi.org/10.1515/jaa-2021-2046.

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Abstract In this paper, we obtain some fixed point theorems for multivalued mappings in incomplete metric spaces. Moreover, as motivated by the recent work of Olgun, Minak and Altun [M. Olgun, G. Minak and I. Altun, A new approach to Mizoguchi–Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 2016, 3, 579–587], we improve these theorems with a new generalization contraction condition for multivalued mappings in incomplete metric spaces. This result is a significant generalization of some well-known results in the literature. Also, we provide some examples to show that our main theorems are a generalization of previous results. Finally, we give an application to a boundary value differential equation.

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27

Matkowski, Janusz. "A refinement of the Browder–Göhde–Kirk fixed point theorem and some applications." Journal of Fixed Point Theory and Applications 24, no. 4 (September 27, 2022). http://dx.doi.org/10.1007/s11784-022-00985-2.

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AbstractThe following generalization of the Browder–Göhde–Kirk fixed point theorem is proved: ifCis a nonempty bounded closed and convex subset of a uniformly convex normed spaceXandTis a self-mapping ofCsuch that$$\left\| Tx-Ty\right\| \le \beta \left( \left\| x-y\right\| \right) $$ T x - T y ≤ β x - y for all $$x,y\in C,$$ x , y ∈ C , $$x\ne y,$$ x ≠ y , where a function$$\beta :\left( 0,\infty \right) \rightarrow \left[ 0,\infty \right) $$ β : 0 , ∞ → 0 , ∞ is such that$$ \lim _{t\rightarrow 0+}\frac{\beta \left( t\right) }{t}=1,$$ lim t → 0 + β t t = 1 , thenThas a fixed point. Two modifications of this theorem as well as some accompanying results on Lipschitz-type mappings are given. An application in the theory of $$L^{p}$$ L p -solutions of an iterative functional equation, and some refinements of the Radamacher theorem are proposed.

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