A hybrid iterative scheme for a maximal monotone operator and two countable families of relatively quasi-nonexpansive mappings for generalized mixed equilibrium and variational inequality problems

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Kumam P., Saewan S.

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-s2.0-78650721968&doi=10.1155%2f2010%2f123027&partnerID=40&md5=dfaeb317de5457b3a618c1bae009c4fb

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for an -inverse-strongly monotone operator, the set of solutions of the generalized mixed equilibrium problem and zeros of a maximal monotone operator 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. The results presented in this paper improve and extend some recent results. Copyright ฉ 2010 Siwaporn Saewan and Poom Kumam.

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