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Relevant bibliographies by topics / Asymptotically nonexpansive mappings

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Academic literature on the topic 'Asymptotically nonexpansive mappings'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Asymptotically nonexpansive mappings"

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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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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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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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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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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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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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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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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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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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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Book chapters on the topic "Asymptotically nonexpansive mappings"

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Xiaomin, Chen, Xie Xuping, and Duan Qibin. "Approximation of Implicit Iteration Process for Common Fixed Point of Composite General Asymptotically Nonexpansive Mappings." In Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-31698-2_98.

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Ritika. "Convergence of Three-Step Iterative Process for Generalized Asymptotically Quasi-nonexpansive Mappings in CAT(0) Spaces." In Springer Proceedings in Mathematics & Statistics. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1153-0_22.

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Zhang, Lingmin, Suhong Li, Xin Xiao, and Huijuan Zhao. "Explicit Iteration Scheme with Perturbed Mapping for Common Xed Points of a Nite Family of I -Asymptotically Nonexpansive Mappings." In Communications in Computer and Information Science. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-34041-3_40.

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Nantadilok, Jamnian, and Buraskorn Nuntadilok. "Common Fixed Points of Asymptotically Quasi-Nonexpansive Mappings in CAT(0) Spaces." In Fixed Point Theory and Chaos [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.107186.

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In this manuscript, we investigate and approximate common fixed points of two asymptotically quasi-nonexpansive mappings in CAT0 spaces. Suppose X is a CAT0 space and C is a nonempty closed convex subset of X. Let T1,T2:C→C be two asymptotically quasi-nonexpansive mappings, and F=FT1∩FT2≔x∈C:T1x=T2x=x≠∅. Let αn,βn be sequences in 01. If the sequence {xn} is generated iteratively by xn+1=1−αnxn⊕αnT1nyn,yn=1−βnxn⊕βnT2nxn,n≥1 and x1∈C is the initial element of the sequence (A). We prove that {xn} converges strongly to a common fixed point of T1 and T2 if and only if limn→∞dxnF=0. (B). Suppose αn

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Conference papers on the topic "Asymptotically nonexpansive mappings"

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Wen, Dao-Jun, and Qian-Fen Gong. "Viscosity Approximation Methods for Asymptotically Nonexpansive Mappings in Banach Spaces." In 2011 International Conference on Intelligent Computation Technology and Automation (ICICTA). IEEE, 2011. http://dx.doi.org/10.1109/icicta.2011.85.

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Wang, Yuanheng, and Weiwei Sun. "The Strong Convergence of a New Iterative Algorithm for Asymptotically Nonexpansive Mappings." In 2nd International Conference on Computer and Information Applications (ICCIA 2012). Atlantis Press, 2012. http://dx.doi.org/10.2991/iccia.2012.91.

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Wang, Li-Ping, and Zhuo-Feng Xiao. "Weak and Strong Convergence of Iterative Algorithm with Errors for Three Asymptotically Nonexpansive Mappings." In 2007 International Conference on Machine Learning and Cybernetics. IEEE, 2007. http://dx.doi.org/10.1109/icmlc.2007.4370555.

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Xiaomin, Chen, Feng Yuan-yuan, and Xie Xuping. "Approximation of Composite Implicit Iteration Process for Common Fixed Points of General Asymptotically Nonexpansive Mappings." In 2011 International Conference on Business Computing and Global Informatization (BCGIn). IEEE, 2011. http://dx.doi.org/10.1109/bcgin.2011.87.

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