A system of generalized mixed equilibrium problems, maximal monotone operators, and fixed point problems with application to optimization problems

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Sunthrayuth P., 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-s2.0-84855525602&doi=10.1155%2f2012%2f316276&partnerID=40&md5=b060935206a21d4424e304a0789d7c3a

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others. Copyright ฉ 2012 Pongsakorn Sunthrayuth and Poom Kumam.

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