## Abstract and Applied Analysis

### A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems

Yekini Shehu

#### Abstract

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a solution to a system of generalized mixed equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth using the properties of generalized $f$-projection operator. Using this result, we discuss strong convergence theorem concerning general $H$-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature.

#### Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 861031, 24 pages.

Dates
First available in Project Euclid: 12 August 2011

https://projecteuclid.org/euclid.aaa/1313170945

Digital Object Identifier
doi:10.1155/2010/861031

Mathematical Reviews number (MathSciNet)
MR2754201

Zentralblatt MATH identifier
1215.47085

#### Citation

Shehu, Yekini. A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems. Abstr. Appl. Anal. 2010 (2010), Article ID 861031, 24 pages. doi:10.1155/2010/861031. https://projecteuclid.org/euclid.aaa/1313170945