A viscosity of Cesเro mean approximation methods for a mixed equilibrium, variational inequalities, and fixed point problems

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Kumam P., Jitpeera T., Katchang P.

Publisher: SpringerOpen

Publication year: 2011

Journal: Fixed Point Theory and Applications (1687-1820)

Volume number: 2011

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-78650723250&doi=10.1155%2f2011%2f945051&partnerID=40&md5=e8ab8331e027d1587664569e8da34e7a

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem, the set of solutions of the variational inequality for a β-inverse-strongly monotone mapping, and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Cesro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang (2009), Peng and Yao (2009), Shimizu and Takahashi (1997), and some authors. Copyright © 2011 Thanyarat Jitpeera et al.

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