## 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-$\varphi$-Asymptotically Nonexpansive Mappings in Banach Spaces

#### Abstract

The purpose of this paper is first to introduce the concept of total quasi-$\varphi$-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-$\varphi$-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

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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