Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 961560, 22 pages.

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, and Min Liu

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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.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 961560, 22 pages.

Dates
First available in Project Euclid: 15 February 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1329337714

Digital Object Identifier
doi:10.1155/2012/961560

Mathematical Reviews number (MathSciNet)
MR2861927

Zentralblatt MATH identifier
1244.49025

Citation

Zhu, Jinhua; Chang, Shih-Sen; Liu, Min. Generalized Mixed Equilibrium Problems and Fixed Point Problem for a Countable Family of Total Quasi- $\varphi $ -Asymptotically Nonexpansive Mappings in Banach Spaces. J. Appl. Math. 2012, Special Issue (2012), Article ID 961560, 22 pages. doi:10.1155/2012/961560. https://projecteuclid.org/euclid.jam/1329337714


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