Modified proximal point algorithms for finding a zero point of maximal monotone operators, generalized mixed equilibrium problems and variational inequalities

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

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Publication Details

Author list: Wattanawitoon K., Kumam P.

Publisher: SpringerOpen

Publication year: 2012

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

Volume number: 2012

ISSN: 1025-5834

eISSN: 1029-242X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84870433895&doi=10.1186%2f1029-242X-2012-118&partnerID=40&md5=a41aad145cd321bfe1889f0aeb432e62

Languages: English-Great Britain (EN-GB)

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Abstract

In this article, we prove strong and weak convergence theorems of modified proximal point algorithms for finding a common element of the zero point of maximal monotone operators, the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems and the fixed point set of relatively nonexpansive mappings in a Banach space under difference conditions. Our results modify and improve previous result of Li and Song. ฉ 2012 Wattanawitoon and Kumam; licensee Springer.

Keywords

Generalized mixed equilibrium problems, Maximal monotone operators, Proximal point algorithm, Weak convergence