## Abstract and Applied Analysis

### Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces

#### Abstract

The purpose of this paper is to introduce a new hybrid projection method for finding a common element of the set of common fixed points of two relatively quasi-nonexpansive mappings, the set of the variational inequality for an $\alpha$-inverse-strongly monotone, and the set of solutions of the generalized equilibrium problem 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. Base on this result, we also get some new and interesting results. The results in this paper generalize, extend, and unify some well-known strong convergence results in the literature.

#### Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 734126, 25 pages.

Dates
First available in Project Euclid: 2 March 2010

https://projecteuclid.org/euclid.aaa/1267538585

Digital Object Identifier
doi:10.1155/2010/734126

Mathematical Reviews number (MathSciNet)
MR2584619

Zentralblatt MATH identifier
1195.47044

#### Citation

Saewan, Siwaporn; Kumam, Poom; Wattanawitoon, Kriengsak. Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces. Abstr. Appl. Anal. 2010 (2010), Article ID 734126, 25 pages. doi:10.1155/2010/734126. https://projecteuclid.org/euclid.aaa/1267538585

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