Abstract and Applied Analysis

A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed-Point Problems, and Variational Inequalities

Jian-Wen Peng, Soon-Yi Wu, and Jen-Chih Yao

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Abstract

We introduce a new iterative scheme based on extragradient method and viscosity approximation method for finding a common element of the solutions set of a system of equilibrium problems, fixed point sets of an infinite family of nonexpansive mappings, and the solution set of a variational inequality for a relaxed cocoercive mapping in a Hilbert space. We prove strong convergence theorem. The results in this paper unify and generalize some well-known results in the literature.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 428293, 27 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620749

Digital Object Identifier
doi:10.1155/2010/428293

Mathematical Reviews number (MathSciNet)
MR2672192

Zentralblatt MATH identifier
1206.47080

Citation

Peng, Jian-Wen; Wu, Soon-Yi; Yao, Jen-Chih. A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed-Point Problems, and Variational Inequalities. Abstr. Appl. Anal. 2010 (2010), Article ID 428293, 27 pages. doi:10.1155/2010/428293. https://projecteuclid.org/euclid.aaa/1288620749


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