A general iterative algorithm for generalized mixed equilibrium problems and variational inclusions approach to variational inequalities

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Authors/Editors

POOM KUMAM

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Publication Details

Author list: Kumam P., Jitpeera T.

Publisher: Hindawi

Publication year: 2011

Journal: International Journal of Mathematics and Mathematical Sciences (0161-1712)

Volume number: 2011

ISSN: 0161-1712

eISSN: 1687-0425

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-79959281643&doi=10.1155%2f2011%2f619813&partnerID=40&md5=2065d61e2cc0558a08dca4af34c952cd

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Marino and Xu (2006), Su et al. (2008), Klin-eam and Suantai (2009), Tan and Chang (2011), and some other authors. Copyright 2011 Thanyarat Jitpeera and Poom Kumam.

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