## Abstract and Applied Analysis

### Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi-$\mathbf{\varphi }$-Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces

#### Abstract

The main purpose of this paper is by using a hybrid algorithm to find a common element of the set of solutions for a generalized mixed equilibrium problem, the set of solutions for variational inequality problems, and the set of common fixed points for a infinite family of total quasi-$\varphi$-asymptotically nonexpansive multivalued mapping in a real uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results announced by some authors.

#### Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 147915, 16 pages.

Dates
First available in Project Euclid: 1 April 2013

https://projecteuclid.org/euclid.aaa/1364845149

Digital Object Identifier
doi:10.1155/2012/147915

Mathematical Reviews number (MathSciNet)
MR2922952

Zentralblatt MATH identifier
1318.47096

#### Citation

Tan, J. F.; Chang, S. S. Strong Convergence Theorems for a Generalized Mixed Equilibrium Problem and a Family of Total Quasi- $\mathbf{\varphi }$ -Asymptotically Nonexpansive Multivalued Mappings in Banach Spaces. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 147915, 16 pages. doi:10.1155/2012/147915. https://projecteuclid.org/euclid.aaa/1364845149

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