Common solutions of generalized mixed equilibrium problems, variational inclusions, and common fixed points for nonexpansive semigroups and strictly pseudocontractive mappings

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Kumam P., Hamphries U., Katchang P.

Publisher: Hindawi

Publication year: 2011

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

Volume number: 2011

ISSN: 1110-757X

eISSN: 1687-0042

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-81755161258&doi=10.1155%2f2011%2f953903&partnerID=40&md5=9cbfa9e88b884e1e71cb6b788850fc1b

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above four sets under some mind conditions. Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem was obtained. Our results improve and extend the corresponding results of Martinez-Yanes and Xu (2006), Shehu (2011), Zhang et al. (2008), and many authors. Copyright ฉ 2011 Poom Kumam et al.

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