Abstract and Applied Analysis

A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems

Uamporn Witthayarat, Thanyarat Jitpeera, and Poom Kumam

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Abstract

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 206345, 29 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475865

Digital Object Identifier
doi:10.1155/2012/206345

Mathematical Reviews number (MathSciNet)
MR2984030

Zentralblatt MATH identifier
06116344

Citation

Witthayarat, Uamporn; Jitpeera, Thanyarat; Kumam, Poom. A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems. Abstr. Appl. Anal. 2012 (2012), Article ID 206345, 29 pages. doi:10.1155/2012/206345. https://projecteuclid.org/euclid.aaa/1364475865


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