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Strong convergence theorems for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups  [cached]
Yongfu Su,Xiaolong Qin
Fixed Point Theory and Applications , 2006, DOI: 10.1155/fpta/2006/96215
Abstract: Strong convergence theorems are obtained from modified Halpern iterative scheme for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups, respectively. Our results extend and improve the recent ones announced by Nakajo, Takahashi, Kim, Xu, and some others.
Strong convergence theorems for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups  [cached]
Su Yongfu,Qin Xiaolong
Fixed Point Theory and Applications , 2006,
Abstract: Strong convergence theorems are obtained from modified Halpern iterative scheme for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups, respectively. Our results extend and improve the recent ones announced by Nakajo, Takahashi, Kim, Xu, and some 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).
An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces  [cached]
Wang Shenghua,Yu Lanxiang,Guo Baohua
Fixed Point Theory and Applications , 2008,
Abstract: Let be a nonempty closed convex subset of a reflexive Banach space with a weakly continuous dual mapping, and let be an infinite countable family of asymptotically nonexpansive mappings with the sequence satisfying for each , , and for each . In this paper, we introduce a new implicit iterative scheme generated by and prove that the scheme converges strongly to a common fixed point of , which solves some certain variational inequality.
Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi- -Asymptotically Nonexpansive Mappings in Banach Spaces
Jinhua Zhu,Shih-Sen Chang,Min Liu
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/961560
Abstract: The purpose of this paper is first to introduce the concept of total quasi--asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases and then to use a hybrid algorithm to introduce a new iterative scheme for finding a common element of the set of solutions for a system of generalized mixed equilibrium problems and the set of common fixed points for a countable family of total quasi--asymptotically nonexpansive mappings. Under suitable conditions some strong convergence theorems are established in an uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in the paper improve and extend some recent results.
An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces  [cached]
Shenghua Wang,Lanxiang Yu,Baohua Guo
Fixed Point Theory and Applications , 2008, DOI: 10.1155/2008/350483
Abstract: Let K be a nonempty closed convex subset of a reflexive Banach space E with a weakly continuous dual mapping, and let {Ti}i=1 ¢ be an infinite countable family of asymptotically nonexpansive mappings with the sequence {kin} satisfying kin ¢ ‰ ¥1 for each i=1,2, ¢ € |, n=1,2, ¢ € |, and limn ¢ ’ ¢ kin=1 for each i=1,2, ¢ € |. In this paper, we introduce a new implicit iterative scheme generated by {Ti}i=1 ¢ and prove that the scheme converges strongly to a common fixed point of {Ti}i=1 ¢ , which solves some certain variational inequality.
Strong Convergence Theorems for Countable Families of Uniformly Quasi--Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems
Siwaporn Saewan,Poom Kumam
Abstract and Applied Analysis , 2011, DOI: 10.1155/2011/701675
Abstract: The purpose of this paper is to present a new hybrid block iterative scheme by the generalized - projection method for finding a common element of the fixed point set for a countable family of uniformly quasi--asymptotically nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new iterative scheme converges strongly to a common element of the aforementioned sets. The results presented in this paper improve and extend important recent results in the literature.
Strong Convergence Theorems for a Countable Family of Total Quasi--Asymptotically Nonexpansive Nonself Mappings
Liang-cai Zhao,Shih-sen Chang
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/136134
Abstract: The purpose of this paper is to introduce a class of total quasi-ϕ-asymptotically nonexpansive-nonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the corresponding results announced by some authors recently.
Strong convergence theorems for a countable family of total quasi-phi-asymptotically nonexpansive nonself mappings  [PDF]
Zhaoli Ma,Lin Wang
International Mathematical Forum , 2013,
Abstract: In this paper, we introduce a class of total quasi-φ-asymptotically nonexpansivenonself mappings which contain several kinds of mappings as its special cases, andobtain some strong convergence theorems for this type of mappings in Banach spacesunder some mild control conditions. The results presented in this paper improveand extend some recent corresponding results.
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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