A new iterative scheme for generalized mixed equilibrium, variational inequality problems, and a zero point of maximal monotone operators

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Wattanawitoon K., Kumam P.

Publisher: Hindawi

Publication year: 2012

Journal: Journal of Applied Mathematics (1110-757X)

Volume number: 2012

ISSN: 1110-757X

eISSN: 1687-0042

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84858111136&doi=10.1155%2f2012%2f692829&partnerID=40&md5=b8005bde426db018ec3fb0f57753d2ae

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this paper is to introduce a new iterative scheme for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of solutions of variational inequality problems, the zero point of maximal monotone operators, and the set of two countable families of quasi-φ-nonexpansive mappings in Banach spaces. Moreover, the strong convergence theorems of this method are established under the suitable conditions of the parameter imposed on the algorithm. Finally, we apply our results to finding a zero point of inverse-strongly monotone operators and complementarity problems. Our results presented in this paper improve and extend the recently results by many others. Copyright © 2012 Kriengsak Wattanawitoon and Poom Kumam.

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