Journal of Applied Mathematics

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

Zhaoli Ma, Lin Wang, and Yunhe Zhao

Full-text: Open access

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- ϕ -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

Permanent link to this document
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


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