Strong convergence for generalized equilibrium problems, fixed point problems and relaxed cocoercive variational inequalities

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Kumam P., Jaiboon C.

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-s2.0-77951493261&doi=10.1155%2f2010%2f728028&partnerID=40&md5=0f109269114533fa56da01a415ba64ce

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a new iterative scheme for finding the common element of the set of solutions of the generalized equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of the variational inequality problems for a relaxed (u,v)-cocoercive and ℰ-Lipschitz continuous mapping in a real Hilbert space. Then, we prove the strong convergence of a common element of the above three sets under some suitable conditions. Our result can be considered as an improvement and refinement of the previously known results. © 2010 C. Jaiboon and P. Kumam.

Keywords