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Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings  [cached]
Saeidi Shahram
Fixed Point Theory and Applications , 2010,
Abstract: We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides and Ramírez (2001), and Li and Sims (2002).
Ergodic Retractions for Families of Asymptotically Nonexpansive Mappings  [cached]
Shahram Saeidi
Fixed Point Theory and Applications , 2010, DOI: 10.1155/2010/281362
Abstract: We prove some theorems for the existence of ergodic retractions onto the set of common fixed points of a family of asymptotically nonexpansive mappings. Our results extend corresponding results of Benavides and Ramírez (2001), and Li and Sims (2002).
Strong Convergence of Hybrid Algorithm for Asymptotically Nonexpansive Mappings in Hilbert Spaces
Juguo Su,Yuchao Tang,Liwei Liu
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/170540
Abstract: The hybrid algorithms for constructing fixed points of nonlinear mappings have been studied extensively in recent years. The advantage of this methods is that one can prove strong convergence theorems while the traditional iteration methods just have weak convergence. In this paper, we propose two types of hybrid algorithm to find a common fixed point of a finite family of asymptotically nonexpansive mappings in Hilbert spaces. One is cyclic Mann's iteration scheme, and the other is cyclic Halpern's iteration scheme. We prove the strong convergence theorems for both iteration schemes.
Strong Convergence to Common Fixed Points for Countable Families of Asymptotically Nonexpansive Mappings and Semigroups  [cached]
Wattanawitoon Kriengsak,Kumam Poom
Fixed Point Theory and Applications , 2010,
Abstract: We prove strong convergence theorems for countable families of asymptotically nonexpansive mappings and semigroups in Hilbert spaces. Our results extend and improve the recent results of Nakajo and Takahashi (2003) and of Zegeye and Shahzad (2008) from the class of nonexpansive mappings to asymptotically nonexpansive mappings.
Strong Convergence Theorem for Two Commutative Asymptotically Nonexpansive Mappings in Hilbert Space  [PDF]
Jianjun Liu,Lili He,Lei Deng
International Journal of Mathematics and Mathematical Sciences , 2008, DOI: 10.1155/2008/236269
Abstract: is a bounded closed convex subset of a Hilbert space , and ∶→ are two asymptotically nonexpansive mappings such that =. We establish a strong convergence theorem for and in Hilbert space by hybrid method. The results generalize and unify many corresponding results.
Browder's Convergence for Uniformly Asymptotically Regular Nonexpansive Semigroups in Hilbert Spaces  [cached]
López Acedo Genaro,Suzuki Tomonari
Fixed Point Theory and Applications , 2010,
Abstract: We give a sufficient and necessary condition concerning a Browder's convergence type theorem for uniformly asymptotically regular one-parameter nonexpansive semigroups in Hilbert spaces.
Strong Convergence Theorem of Implicit Iteration Process for Generalized Asymptotically Nonexpansive Mappings in Hilbert Space  [PDF]
Lili He,Lei Deng,Jianjun Liu
International Journal of Mathematics and Mathematical Sciences , 2008, DOI: 10.1155/2008/649510
Abstract: Let be a nonempty closed and convex subset of a Hilbert space , let and ∶→ be two commutative generalized asymptotically nonexpansive mappings. We introduce an implicit iteration process of and defined by =0
Strong Convergence Theorem According to Hybrid Methods for Mapping Asymptotically Quasi-Nonexpansive Types  [cached]
Narongrit Puturong
Journal of Mathematics Research , 2010, DOI: 10.5539/jmr.v2n4p3
Abstract: The purpose of this article is to prove strong convergence theorems for mapping of asymptotically quasi-nonexpansive types in a Hilbert space according to hybrid methods. The results obtained in this paper extend and improve upon those recently announced by Qin, X., Su, Y. and Shang, M. (Qin, X. et al., 2008), and many others.
Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings  [PDF]
Watcharaporn Cholamjiak,Suthep Suantai
Abstract and Applied Analysis , 2009, DOI: 10.1155/2009/297565
Abstract: 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).
The super fixed point property for asymptotically nonexpansive mappings  [PDF]
Andrzej Wi?nicki
Mathematics , 2012, DOI: 10.4064/fm217-3-5
Abstract: We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized for commuting families of asymptotically nonexpansive mappings.
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