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Journal articles on the topic 'Asymptotically nonexpansive mappings'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Mukhamedov, Farrukh, and Mansoor Saburov. "On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces." Journal of Applied Mathematics 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/281383.

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We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptoticallyI-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by (C. E. Chidume and E. U. Ofoedu, 2009). We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family

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2

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 Theor

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3

Kirk, W. A., Carlos Martinez Yañez, and Sang Sik Shin. "Asymptotically nonexpansive mappings." Nonlinear Analysis: Theory, Methods & Applications 33, no. 1 (1998): 1–12. http://dx.doi.org/10.1016/s0362-546x(97)00541-5.

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4

Tang, J. F., S. S. Chang, H. W. Joseph Lee та C. K. Chan. "Iterative Algorithm andΔ-Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces". Abstract and Applied Analysis 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/965751.

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The main purpose of this paper is first to introduce the concept of total asymptotically nonexpansive mappings and to prove aΔ-convergence theorem for finding a common fixed point of the total asymptotically nonexpansive mappings and the asymptotically nonexpansive mappings. The demiclosed principle for this kind of mappings in CAT(0) space is also proved in the paper. Our results extend and improve many results in the literature.

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5

Salisu, Sani, Poom Kumam, Songpon Sriwongsa, and Dhananjay Gopalc. "Enriched asymptotically nonexpansive mappings with center zero." Filomat 38, no. 1 (2024): 343–56. http://dx.doi.org/10.2298/fil2401343s.

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In this article, a special mapping, the so-called enriched nonexpansive mapping with center zero and its asymptotic version are introduced and corresponding fixed point properties are investigated in the setting of complete normed spaces. Further, using approximate fixed point sequences, the fixed points of such mappings are analysed where Banach spaces have Kadec-Klee Property. Finally, a convexically enriched nonexpansive mapping is launched as a special case of the studied mappings.

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6

Vijayaraju, P. "Fixed points and their approximations for asymptotically nonexpansive mappings in locally convex spaces." International Journal of Mathematics and Mathematical Sciences 18, no. 2 (1995): 293–98. http://dx.doi.org/10.1155/s0161171295000366.

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We construct an example that the class of asymptotically nonexpansive mappings include properly the class of nonexpansive mappings in locally convex spaces, prove a theorem on the existence of fixed points, and the convergence of the sequence of iterates to a fixed point for asymptotically nonexpansive mappings in locally convex spaces.

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7

Acosta-Portilla, Juan Rafael, and Lizbeth Yolanda Garrido-Ramírez. "On minimal asymptotically nonexpansive mappings." AIMS Mathematics 8, no. 4 (2023): 9416–35. http://dx.doi.org/10.3934/math.2023474.

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<abstract><p>In this paper we present the following two results: 1.- A characterization of the renorming invariant family of asymptotically nonexpansive mappings defined on a convex, closed and bounded set of a Banach space; 2.- A comparison of the renorming invariant family of asymptotically nonexpansive mappings with the renorming invariant family of nonexpansive mappings. Additionally, a series of examples are shown for general and particular cases.</p></abstract>

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8

Chen, Jinzuo, Dingping Wu, and Caifen Zhang. "A New Iterative Scheme of Modified Mann Iteration in Banach Space." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/264909.

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We introduce the modified iterations of Mann's type for nonexpansive mappings and asymptotically nonexpansive mappings to have the strong convergence in a uniformly convex Banach space. We study approximation of common fixed point of asymptotically nonexpansive mappings in Banach space by using a new iterative scheme. Applications to the accretive operators are also included.

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9

Aibinu, M. O., S. C. Thakur, and S. Moyo. "The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings." Journal of Mathematics 2020 (June 6, 2020): 1–12. http://dx.doi.org/10.1155/2020/6876385.

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The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper studies the convergence analysis of the class of asymptotically nonexpansive mappings by the implicit midpoint iterative procedures. The necessary conditions for the convergence of the class of asymptotically nonexpansive mappings are established, by using a well-known iterative algorithm which plays important roles in the computation of fixed points of non

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10

Vijayaraju, P. "Fixed point theorems for a sum of two mappings in locally convex spaces." International Journal of Mathematics and Mathematical Sciences 17, no. 4 (1994): 681–86. http://dx.doi.org/10.1155/s0161171294000967.

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Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings. In this paper, we prove by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces. These results extend a result of Ca

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11

Laowang, W., and B. Panyanak. "A Note on Common Fixed Point Results in Uniformly Convex Hyperbolic Spaces." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/503731.

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It is shown that the notion of mappings satisfying condition(K)introduced by Akkasriworn et al. (2012) is weaker than the notion of asymptotically quasi-nonexpansive mappings in the sense of Qihou (2001) and is weaker than the notion of pointwise asymptotically nonexpansive mappings in the sense of Kirk and Xu (2008). We also obtain a common fixed point for a commuting pair of a mapping satisfying condition(K)and a multivalued mapping satisfying condition(Cλ)for someλ∈(0,1). Our results properly contain the results of Abkar and Eslamian (2012), Akkasriworn et al. (2012), and many others.

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12

ALFURAIDAN, M. R., and M. A. KHAMSI. "FIBONACCI–MANN ITERATION FOR MONOTONE ASYMPTOTICALLY NONEXPANSIVE MAPPINGS." Bulletin of the Australian Mathematical Society 96, no. 2 (2017): 307–16. http://dx.doi.org/10.1017/s0004972717000120.

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We extend the results of Schu [‘Iterative construction of fixed points of asymptotically nonexpansive mappings’, J. Math. Anal. Appl.158 (1991), 407–413] to monotone asymptotically nonexpansive mappings by means of the Fibonacci–Mann iteration process $$\begin{eqnarray}x_{n+1}=t_{n}T^{f(n)}(x_{n})+(1-t_{n})x_{n},\quad n\in \mathbb{N},\end{eqnarray}$$ where $T$ is a monotone asymptotically nonexpansive self-mapping defined on a closed bounded and nonempty convex subset of a uniformly convex Banach space and $\{f(n)\}$ is the Fibonacci integer sequence. We obtain a weak convergence result in $L_

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13

Shi, Luo Yi, Ru Dong Chen, and Yu Jing Wu. "-Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/251705.

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New △-convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained. Consider an asymptotically nonexpansive self-mapping of a closed convex subset of a CAT(0) space . Consider the iteration process , where is arbitrary and or for , where . It is shown that under certain appropriate conditions on △-converges to a fixed point of .

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14

Kiziltunc, Hukmi, and Yunus Purtas. "On weak and strong convergence of an explicit iteration process for a total asymptotically quasi-I-nonexpansive mapping in Banach space." Filomat 28, no. 8 (2014): 1699–710. http://dx.doi.org/10.2298/fil1408699k.

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In this paper, we introduce a new class of Lipschitzian maps and prove some weak and strong convergence results for explicit iterative process using a more satisfactory definition of self mappings. Our results approximate common fixed point of a total asymptotically quasi-I-nonexpansive mapping T and a total asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a Banach space.

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15

Kaczor, Wieslawa. "Fixed points of asymptotically regular nonexpansive mappings on nonconvex sets." Abstract and Applied Analysis 2003, no. 2 (2003): 83–91. http://dx.doi.org/10.1155/s1085337503205054.

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It is shown that ifXis a Banach space andCis a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets{Ci:1≤i≤n }ofX, and eachCihas the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping ofChas a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach spaces with Opial's property.

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16

Karapınar, Erdal, Hero Salahifard, and S. Mansour Vaezpour. "Demiclosedness Principle for Total Asymptotically Nonexpansive Mappings inCAT(0)Spaces." Journal of Applied Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/738150.

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We prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework ofCAT(0)spaces. Our results generalize, extend, and unify the corresponding results on the topic in the literature.

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17

Agwu, Imo Kalu, Donatus Ikechi Igbokwe, and Nathenial C. Ukeje. "Convergence of a Three-step Iteration Scheme to the Common Fixed Points of Mixed-Type Total Asymtotically Nonexpansive Mappings in Uniformly Convex Banach Spaces." European Journal of Mathematical Analysis 1, no. 1 (2021): 45–67. http://dx.doi.org/10.28924/ada/ma.1.45.

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We propose a three-step iteration scheme of hybrid mixed-type for three total asymptotically nonexpansive self mappings and three total asymptotically nonexpansive nonself mappings. In addition, we establish some weak convergence theorems of the scheme to the common fixed point of the mappings in uniformly convex Banach spaces. Our results extend and generalize numerous results currently in literature.

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18

Qin, Xiaolong, та Lin Wang. "On Asymptotically Quasi-ϕ-Nonexpansive Mappings in the Intermediate Sense". Abstract and Applied Analysis 2012 (2012): 1–13. http://dx.doi.org/10.1155/2012/636217.

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A projection iterative process is investigated for the class of asymptotically quasi-ϕ-nonexpansive mappings in the intermediate sense. Strong convergence theorems of common fixed points of a family of asymptotically quasi-ϕ-nonexpansive mappings in the intermediate sense are established in the framework of Banach spaces.

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19

Kim, Tae-Hwa, and Hong-Kun Xu. "Remarks on asymptotically nonexpansive mappings." Nonlinear Analysis: Theory, Methods & Applications 41, no. 3-4 (2000): 405–15. http://dx.doi.org/10.1016/s0362-546x(98)00284-3.

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20

Saluja, G. S. "Weak Convergence Theorems for Asymptotically Nonexpansive Mappings and Total Asymptotically Nonexpansive Non-Self Mappings." Sohag Journal of Mathematics 4, no. 2 (2017): 49–57. http://dx.doi.org/10.18576/sjm/040204.

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21

El Bazi, Hamza, and Abdellatif Sadrati. "Fixed point theorem for mixed monotone nearly asymptotically nonexpansive mappings and applications to integral equations." Electronic Journal of Differential Equations 2022, no. 01-87 (2022): 66. http://dx.doi.org/10.58997/ejde.2022.66.

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This work concerns the existence of a fixed point for mixed monotone nearly asymptotically nonexpansive mappings. We extend and generalize some well-known results concerning nearly asymptotically nonexpansive mappings in a uniformly convex hyperbolic metric space. As application of our results, we study the existence of solutions for an integral equation.

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22

Su, Yongfu, and Xiaolong Qin. "Strong convergence theorems for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups." Fixed Point Theory and Applications 2006 (2006): 1–12. http://dx.doi.org/10.1155/fpta/2006/96215.

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23

Kalsoom, Amna, Hafiz Fukhar-Ud-Din, and Sara Najib. "Proximal point algorithms involving Cesàro type mean of total asymptotically nonexpansive mappings in CAT(0) spaces." Filomat 32, no. 12 (2018): 4165–76. http://dx.doi.org/10.2298/fil1812165k.

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In this paper, we extend the proximal point algorithm proposed by Chang et al.[8] for total asymptotically nonexpansive mapping in CAT(0) spaces. We also demonstrate the ?-convergence and strong convergence to a common element of the set of minimizers of a convex function and the set of fixed points of the Ces?ro type mean of total asymptotically nonexpansive mappings in CAT(0) spaces.

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24

Verma, Anurag, and B. P. Tripathi. "Approximation of common fixed point of two asymptotically nonexpansive mappings in the intermediate sense for a new iteration process in CAT(0) spaces." Annals of Mathematics and Computer Science 24 (June 23, 2024): 85–98. http://dx.doi.org/10.56947/amcs.v24.341.

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In this paper, we establish strong and ∆−convergence for a new iteration process containing two asymptotically nonexpansive mappings in the intermediate sense which is broader than the class of asymptotically nonexpansive mappings in the context of CAT(0) spaces. Our results extend, generalize, and improve many well-known results in the literature.

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25

Temir, Seyit. "Convergence theorems of a scheme for I-asymptotically quasi-nonexpansive type mapping in Banach space." Publications de l'Institut Math?matique (Belgrade) 97, no. 111 (2015): 239–51. http://dx.doi.org/10.2298/pim130818001t.

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Let X be a Banach space. Let K be a nonempty subset of X. Let T : K ? K be an I-asymptotically quasi-nonexpansive type mapping and I : K ? K be an asymptotically quasi-nonexpansive type mappings in the Banach space. Our aim is to establish the necessary and sufficient conditions for the convergence of the Ishikawa iterative sequences with errors of an I-asymptotically quasi-nonexpansive type mappping in Banach spaces to a common fixed point of T and I. Also, we study the convergence of the Ishikawa iterative sequences to common fixed point for nonself I-asymptotically quasinonexpansive type ma

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26

Radhakrishnan, M., and S. Rajesh. "Existence ofixed points for pointwise eventually asymptotically nonexpansive mappings." Applied General Topology 20, no. 1 (2019): 119. http://dx.doi.org/10.4995/agt.2019.10360.

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<p>Kirk introduced the notion of pointwise eventually asymptotically non-expansive mappings and proved that uniformly convex Banach spaces have the fixed point property for pointwise eventually asymptotically non expansive maps. Further, Kirk raised the following question: “Does a Banach space X have the fixed point property for pointwise eventually asymptotically nonexpansive mappings when ever X has the fixed point property for nonexpansive mappings?”. In this paper, we prove that a Banach space X has the fixed point property for pointwise eventually asymptotically nonexpansive maps if

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27

Thianwan, Tanakit. "Mixed Type Algorithms for Asymptotically Nonexpansive Mappings in Hyperbolic Spaces." European Journal of Pure and Applied Mathematics 14, no. 3 (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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28

Saluja, Gurucharan Singh. "Strong Convergence Theorems for Hybrid Mixed Type Nonlinear Mappings in Banach Spaces." Annals of West University of Timisoara - Mathematics and Computer Science 56, no. 1 (2018): 136–48. http://dx.doi.org/10.2478/awutm-2018-0009.

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Abstract In this paper, we introduce a new two-step iteration scheme of hybrid mixed type for two asymptotically nonexpansive self mappings and two asymptotically nonexpansive non-self mappings in the intermediate sense and establish some strong convergence theorems for mentioned scheme and mappings in Banach spaces. Our results extend and generalize the corresponding results recently announced by Wei and Guo [16] (Comm. Math. Res. 31(2015), 149-160) and many others.

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29

Pineda, Maria A. Japón. "The fixed-point property in Banach spaces containing a copy ofc0." Abstract and Applied Analysis 2003, no. 3 (2003): 183–92. http://dx.doi.org/10.1155/s1085337503203055.

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We prove that every Banach space containing an isomorphic copy ofc0fails to have the fixed-point property for asymptotically nonexpansive mappings with respect to some locally convex topology which is coarser than the weak topology. If the copy ofc0is asymptotically isometric, this result can be improved, because we can prove the failure of the fixed-point property for nonexpansive mappings.

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30

Saluja, G. S. "Strong convergence theorem for two asymptotically quasi-nonexpansive mappings with errors in Banach space." Tamkang Journal of Mathematics 38, no. 1 (2007): 85–92. http://dx.doi.org/10.5556/j.tkjm.38.2007.96.

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In this paper, we study strong convergence of common fixed points of two asymptotically quasi-nonexpansive mappings and prove that if $K$ is a nonempty closed convex subset of a real Banach space $E$ and let $ S, T\colon K\to K $ be two asymptotically quasi-nonexpansive mappings with sequences $ \{u_n\}$, $\{v_n\}\subset [0,\infty) $ such that $ \sum_{n=1}^{\infty}u_n

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31

Rashid, Maliha, Amna Kalsoom, Shao-Wen Yao, Abdul Ghaffar, and Mustafa Inc. "Convergence Results for Total Asymptotically Nonexpansive Monotone Mappings in Modular Function Spaces." Journal of Function Spaces 2021 (July 15, 2021): 1–7. http://dx.doi.org/10.1155/2021/9982168.

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In this article, we consider an extensive class of monotone nonexpansive mappings. We use S -iteration to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the settings of modular function space.

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32

Weng, Shengquan, and Dingping Wu. "Convergence Theorems of Modified Proximal Algorithms for Asymptotical Quasi-nonexpansive Mappings in CAT(0) Spaces." Journal of Mathematics Research 10, no. 2 (2018): 66. http://dx.doi.org/10.5539/jmr.v10n2p66.

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In this paper, a new modified proximal point algorithm involving fixed point iterates of a finite number of asymptotically quasi-nonexpansive mappings in $CAT(0)$ spaces is proposed and been proved for the existence of a sequence generated by our iterative process converging to a minimizer of a convex function and a commen fixed point of a finite number of asymptotically quasi-nonexpansive mappings.

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33

Li, Gang, and Jong Kyu Kim. "Nonlinear ergodic theorems for asymptotically almost nonexpansive curves in a Hilbert space." Abstract and Applied Analysis 5, no. 3 (2000): 147–58. http://dx.doi.org/10.1155/s1085337500000312.

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We introduce the notion of asymptotically almost nonexpansive curves which include almost-orbits of commutative semigroups of asymptotically nonexpansive type mappings and study the asymptotic behavior and prove nonlinear ergodic theorems for such curves. As applications of our main theorems, we obtain the results on the asymptotic behavior and ergodicity for a commutative semigroup of non-Lipschitzian mappings with nonconvex domains in a Hilbert space.

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34

Veysel, Nezir, and İlgar Sümeyye. "A Large Class in Köthe-Toeplitz Duals of Cesàro Difference Sequence Spaces with Fixed Point Property for Asymptotically Nonexpansive Mappings." Journal of Scientific and Engineering Research 8, no. 10 (2021): 117–24. https://doi.org/10.5281/zenodo.10618711.

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<strong>Abstract</strong> In 1970, Cesàro Sequence Spaces was introduced by Shiue. In 1981, Kızmaz defined difference sequence spaces for ,  and . Then, in 1983, Orhan introduced Cesàro Difference Sequence Spaces. In this study, first we discuss the fixed point property for these spaces. Then, we recall that Goebel and Kuczumow showed that there exists a very large class of closed, bounded, convex subsets in Banach space of absolutely summable scalar sequences,  with fixed point property for nonexpansive mappings. In 2004, Kaczor and Prus investigated if similar result

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35

Chang, S. S. "Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings." Proceedings of the American Mathematical Society 129, no. 3 (2000): 845–53. http://dx.doi.org/10.1090/s0002-9939-00-05988-8.

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36

Cholamjiak, Watcharaporn, and Suthep Suantai. "Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings." Abstract and Applied Analysis 2009 (2009): 1–16. http://dx.doi.org/10.1155/2009/297565.

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We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003).

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37

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 fi

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38

Lin, Pei-Kee. "Asymptotic behavior for asymptotically nonexpansive mappings." Nonlinear Analysis: Theory, Methods & Applications 26, no. 6 (1996): 1137–41. http://dx.doi.org/10.1016/0362-546x(94)00283-n.

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39

Saluja, G. S. "Hybrid mixed type iteration scheme for asymptotically nonexpansive mappings and total asymptotically nonexpansive non-self mappings." Mathematica Moravica 20, no. 2 (2016): 131–41. http://dx.doi.org/10.5937/matmor1602131s.

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40

Saejung, Satit, Suthep Suantai, and Pongsakorn Yotkaew. "A Note on “Common Fixed Point of Multistep Noor Iteration with Errors for a Finite Family of Generalized Asymptotically Quasi-Nonexpansive Mappings”." Abstract and Applied Analysis 2009 (2009): 1–9. http://dx.doi.org/10.1155/2009/283461.

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The purpose of this paper is to give a general and short principle for proving some convergence results of certain types of iterative sequences. A small gap in the paper by Imnang and Suantai (2009) is discussed and corrected. Finally, we prove that the generalized asymptotically quasi-nonexpansive mappings in the sense of Lan (2006) are nothing but asymptotically quasi-nonexpansive. Hence several results concerning these mappings become a special case of the known ones.

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41

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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42

KHAN, ABDUL RAHIM, MUJAHID ABBAS, and YEKINI SHEHU. "A general convergence theorem for multiple-set split feasibility problem in Hilbert spaces." Carpathian Journal of Mathematics 31, no. 3 (2015): 349–57. http://dx.doi.org/10.37193/cjm.2015.03.11.

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We establish strong convergence result of split feasibility problem for a family of quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces.

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43

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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44

Abdou, Afrah A. N., та Mohamed A. Khamsi. "Periodic Points of Modular Firmly Mappings in the Variable Exponent Sequence Spaces ℓp(·)". Mathematics 9, № 19 (2021): 2418. http://dx.doi.org/10.3390/math9192418.

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In this work, we investigate the existence of periodic points of mappings defined on nonconvex domains within the variable exponent sequence spaces ℓp(·). In particular, we consider the case of modular firmly nonexpansive and modular firmly asymptotically nonexpansive mappings. These kinds of results have never been obtained before.

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45

Tang, Yuchao, and Liwei Liu. "Note on some results for asymptotically pseudocontractive mappings and asymptotically nonexpansive mappings." Fixed Point Theory and Applications 2006 (2006): 1–8. http://dx.doi.org/10.1155/fpta/2006/24978.

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46

Ceng, Lu-Chuan, Yekini Shehu, and Jen-Chih Yao. "Modified Mann Subgradient-like Extragradient Rules for Variational Inequalities and Common Fixed Points Involving Asymptotically Nonexpansive Mappings." Mathematics 10, no. 5 (2022): 779. http://dx.doi.org/10.3390/math10050779.

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In a real Hilbert space, we aim to investigate two modified Mann subgradient-like methods to find a solution to pseudo-monotone variational inequalities, which is also a common fixed point of a finite family of nonexpansive mappings and an asymptotically nonexpansive mapping. We obtain strong convergence results for the sequences constructed by these proposed rules. We give some examples to illustrate our analysis.

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47

Gu, Feng. "Implicit iterative process for common fixed point of a finite family of asymptotically nonexpansive mappings." Studia Scientiarum Mathematicarum Hungarica 45, no. 2 (2008): 235–50. http://dx.doi.org/10.1556/sscmath.2007.1044.

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The purpose of this paper is to study the weak and strong convergence of implicit iteration process to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [1,2,4–9,11–15].

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48

Kalsoom, Amna, Maliha Rashid, Tian-Chuan Sun, et al. "Fixed Points of Monotone Total Asymptotically Nonexpansive Mapping in Hyperbolic Space via New Algorithm." Journal of Function Spaces 2021 (July 28, 2021): 1–10. http://dx.doi.org/10.1155/2021/8482676.

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In this article, we consider an extensive class of monotone nonexpansive mappings and introduce a new iteration algorithm to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the framework of hyperbolic space. Faster convergence and stability results are proved for that iteration; also, fixed point is approximated numerically in a nontrivial example by using MATLAB.

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49

Khan, Safeer Hussain, and Nawab Hussain. "Convergence theorems for nonself asymptotically nonexpansive mappings." Computers & Mathematics with Applications 55, no. 11 (2008): 2544–53. http://dx.doi.org/10.1016/j.camwa.2007.10.007.

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50

Krüppel, Manfred, and Jaroslaw Górnicki. "An ergodic theorem for asymptotically nonexpansive mappings." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 124, no. 1 (1994): 23–31. http://dx.doi.org/10.1017/s0308210500029176.

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The purpose of this paper is to prove the following (nonlinear) mean ergodic theorem: Let E be a uniformly convex Banach space, let C be a nonempty bounded closed convex subset of E and let T: C → C be an asymptotically nonexpansive mapping. Ifexists uniformly in r = 0, 1, 2,…, then the sequence {Tnx} is strongly almost-convergent to a fixed point y of T, that is,uniformly in i = 0, 1, 2, ….

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