Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces

The purpose of this paper is first to introduce the concept of total quasi-ϕ-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...

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Main Authors: Jinhua Zhu, Shih-Sen Chang, Min Liu
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/961560
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spelling doaj-eae2d66c4742491ca10f9d825776a06e2020-11-24T22:18:17ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/961560961560Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach SpacesJinhua Zhu0Shih-Sen Chang1Min Liu2Department of Mathematics, Yibin University, Yibin, Sichuan 644007, ChinaDepartment of Mathematics, College of Statistics and Mathematics, Yunnan University of Finance and Economics, Yunnan, Kunming 650221, ChinaDepartment of Mathematics, Yibin University, Yibin, Sichuan 644007, ChinaThe purpose of this paper is first to introduce the concept of total quasi-ϕ-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-ϕ-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.http://dx.doi.org/10.1155/2012/961560
collection DOAJ
language English
format Article
sources DOAJ
author Jinhua Zhu
Shih-Sen Chang
Min Liu
spellingShingle Jinhua Zhu
Shih-Sen Chang
Min Liu
Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces
Journal of Applied Mathematics
author_facet Jinhua Zhu
Shih-Sen Chang
Min Liu
author_sort Jinhua Zhu
title Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces
title_short Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces
title_full Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces
title_fullStr Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces
title_full_unstemmed Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi-ϕ-Asymptotically Nonexpansive Mappings in Banach Spaces
title_sort generalized mixed equilibrium problems and fixed point problem for a countable family of total quasi-ϕ-asymptotically nonexpansive mappings in banach spaces
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description The purpose of this paper is first to introduce the concept of total quasi-ϕ-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-ϕ-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.
url http://dx.doi.org/10.1155/2012/961560
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AT shihsenchang generalizedmixedequilibriumproblemsandfixedpointproblemforacountablefamilyoftotalquasiphasymptoticallynonexpansivemappingsinbanachspaces
AT minliu generalizedmixedequilibriumproblemsandfixedpointproblemforacountablefamilyoftotalquasiphasymptoticallynonexpansivemappingsinbanachspaces
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