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

Journal article

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POOM KUMAM

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Publication Details

Author list: Witthayarat U., Jitpeera T., Kumam P.

Publisher: Hindawi

Publication year: 2012

Journal: Abstract and Applied Analysis (1085-3375)

Volume number: 2012

ISSN: 1085-3375

eISSN: 1687-0409

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84874904565&doi=10.1155%2f2012%2f206345&partnerID=40&md5=a51a5b5f5e7f561f70ed499eaedc691c

Languages: English-Great Britain (EN-GB)

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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. ฉ 2012 Uamporn Witthayarat et al.

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