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 | Zendy

Uamporn Witthayarat | Zendy; Thanyarat Jitpeera | Zendy; Poom Kumam | Zendy

Open Access

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

Author(s) -

Uamporn Witthayarat,

Thanyarat Jitpeera,

Poom Kumam

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/206345

Subject(s) - mathematics , variational inequality , hilbert space , fixed point , minification , norm (philosophy) , method of steepest descent , sequence (biology) , gradient descent , viscosity , mathematical analysis , mathematical optimization , artificial neural network , physics , quantum mechanics , machine learning , biology , political science , computer science , law , genetics

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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