A system of mixed equilibrium problems, a general system of variational inequality problems for relaxed cocoercive, and fixed point problems for nonexpansive semigroup and strictly pseudocontractive mappings

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Kumam P., Katchang P.

Publisher: Hindawi

Publication year: 2012

Journal: Journal of Applied Mathematics (1110-757X)

Volume number: 2012

ISSN: 1110-757X

eISSN: 1687-0042

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84862289378&doi=10.1155%2f2012%2f414831&partnerID=40&md5=a2d5af289e0a40f3eac6cb6d5c2862a6

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (2010) and many others. ฉ Copyright 2012 Poom Kumam and Phayap Katchang.

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