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2012 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, Poom Kumam
Abstr. Appl. Anal. 2012: 1-29 (2012). DOI: 10.1155/2012/206345

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.

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Uamporn Witthayarat. Thanyarat Jitpeera. Poom Kumam. "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 1 - 29, 2012. https://doi.org/10.1155/2012/206345

Information

Published: 2012
First available in Project Euclid: 28 March 2013

zbMATH: 06116344
MathSciNet: MR2984030
Digital Object Identifier: 10.1155/2012/206345

Rights: Copyright © 2012 Hindawi

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