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

Jinhua Zhu, Shih-Sen Chang and Min Liu

Journal of Applied Mathematics, 2012, vol. 2012, 1-22

Abstract:

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

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:961560

DOI: 10.1155/2012/961560

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