## Journal of Applied Mathematics

### Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi-$\varphi$-Asymptotically Nonexpansive Mappings in Banach Spaces

#### Abstract

We introduce an iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of fixed points for countable families of total quasi-$\varphi$-asymptotically nonexpansive mappings in Banach spaces. We prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm in an uniformly smooth and strictly convex Banach space which also enjoys the Kadec-Klee property. The results presented in this paper improve and extend some recent corresponding results.

#### Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 506210, 21 pages.

Dates
First available in Project Euclid: 14 December 2012

https://projecteuclid.org/euclid.jam/1355495167

Digital Object Identifier
doi:10.1155/2012/506210

Mathematical Reviews number (MathSciNet)
MR2935529

Zentralblatt MATH identifier
1244.65077

#### Citation

Ma, Zhaoli; Wang, Lin; Zhao, Yunhe. Strong Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Fixed Point Problems for Total Quasi- $\varphi$ -Asymptotically Nonexpansive Mappings in Banach Spaces. J. Appl. Math. 2012 (2012), Article ID 506210, 21 pages. doi:10.1155/2012/506210. https://projecteuclid.org/euclid.jam/1355495167