Convergence Theorem Based on a New Hybrid Projection Method for Finding a Common Solution of Generalized Equilibrium and Variational Inequality Problems in Banach Spaces

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POOM KUMAM

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Publication Details

Author list: Kumam P., Saewan S., Wattanawitoon K.

Publisher: Hindawi

Publication year: 2010

Journal: Abstract and Applied Analysis (1085-3375)

Volume number: 2010

ISSN: 1085-3375

eISSN: 1687-0409

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-80052651402&doi=10.1155%2f2010%2f734126&partnerID=40&md5=521de18961c987bcb90b39d9d282ddee

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this paper is to introduce a new hybrid projection method for finding a common element of the set of common fixed points of two relatively quasi-nonexpansive mappings, the set of the variational inequality for an -inverse-strongly monotone, and the set of solutions of the generalized equilibrium problem in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Base on this result, we also get some new and interesting results. The results in this paper generalize, extend, and unify some well-known strong convergence results in the literature. Copyright ฉ 2010 Siwaporn Saewan et al.

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