A shrinking projection method for generalized mixed equilibrium problems, variational inclusion problems and a finite family of quasi-nonexpansive mappings

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Jaiboon C., Kumam W., Kumam P., Singta A.

Publisher: SpringerOpen

Publication year: 2010

Journal: Journal of Inequalities and Applications (1025-5834)

Volume number: 2010

ISSN: 1025-5834

eISSN: 1029-242X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-77956780563&doi=10.1155%2f2010%2f458247&partnerID=40&md5=ab0bbdae29b95102266dec5596c63806

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this paper is to consider a shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of fixed points of a finite family of quasi-nonexpansive mappings, and the set of solutions of variational inclusion problems. Then, we prove a strong convergence theorem of the iterative sequence generated by the shrinking projection method under some suitable conditions in a real Hilbert space. Our results improve and extend recent results announced by Peng et al. (2008), Takahashi et al. (2008), S.Takahashi and W. Takahashi (2008), and many others. Copyright ฉ 2010 Wiyada Kumam et al.

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