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2012 Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi- ϕ -Asymptotically Nonexpansive Mappings in Banach Spaces
Jinhua Zhu, Shih-Sen Chang, Min Liu
J. Appl. Math. 2012(SI03): 1-22 (2012). DOI: 10.1155/2012/961560

Abstract

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 forfinding 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.

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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." J. Appl. Math. 2012 (SI03) 1 - 22, 2012. https://doi.org/10.1155/2012/961560

Information

Published: 2012
First available in Project Euclid: 15 February 2012

zbMATH: 1244.49025
MathSciNet: MR2861927
Digital Object Identifier: 10.1155/2012/961560

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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