## 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

Jinhua Zhu, Shih-Sen Chang, and Min Liu

**Full-text: Open access**

#### 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

**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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