Existence and approximation for a solution of a generalized equilibrium problem on the dual space of a Banach space

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

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Publication Details

Author list: Phuangphoo P., Kumam P.

Publisher: SpringerOpen

Publication year: 2013

Journal: Fixed Point Theory and Applications (1687-1820)

Volume number: 2013

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84902595250&doi=10.1186%2f1687-1812-2013-264&partnerID=40&md5=8a724cb753d88ab8f802f2840dec4a07

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we first prove the existence of a solution for a generalized equilibrium problem with a bifunction defined on the dual space in a Banach space setting. Second, by the virtue of this result, we construct the hybrid projection method for solving a solution of a generalized equilibrium problem. Consequently, we establish the strong convergence theorem by using sunny generalized nonexpansive retraction in the dual of Banach spaces. ฉ2013 Phuangphoo and Kumam; licensee Springer.

Keywords

A bifunction defined on the dual space, A generalized equilibrium problem, The hybrid projection method