Abstract and Applied Analysis

A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems

Abstract

We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for an $\alpha$-inverse-strongly monotone operator, the set of solutions of the generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2 uniformly convex and uniformly smooth Banach space. The results presented in this paper improve and extend some recent results.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 123027, 31 pages.

Dates
First available in Project Euclid: 12 August 2011

https://projecteuclid.org/euclid.aaa/1313170913

Digital Object Identifier
doi:10.1155/2010/123027

Mathematical Reviews number (MathSciNet)
MR2735003

Zentralblatt MATH identifier
1204.65062

Citation

Saewan, Siwaporn; Kumam, Poom. A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems. Abstr. Appl. Anal. 2010 (2010), Article ID 123027, 31 pages. doi:10.1155/2010/123027. https://projecteuclid.org/euclid.aaa/1313170913