A strong convergence theorem based on a relaxed extragradient method for generalized equilibrium problems

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

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Publication Details

Author list: Onjai-uea N., Jaiboon C., Kumam P.

Publisher: Hikari

Publication year: 2010

Journal: Applied Mathematical Sciences (1312-885X)

Volume number: 4

Issue number: 13-16

Start page: 691

End page: 708

Number of pages: 18

ISSN: 1312-885X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-77953332772&partnerID=40&md5=5928a2165d0ebf02d273f03b4a86001c

Languages: English-Great Britain (EN-GB)

Abstract

In this paper, we introduce a new relaxed extragradient viscosity approximation method for finding the common element of the set of solutions of a generalized equilibrium problems, the set of common fixed points of a finite family of nonexpansive mappings and the set solutions of the variational inequality for an inverse-strongly monotone mapping. Then, we prove a strong convergence theorem of the proposed iterative scheme in a real Hilbert spaces. Our result extend and improve many others in the literature area.

Keywords

Generalized equilibrium problem