An Iterative method for solving a system of mixed equilibrium problems, system of quasivariational inclusions, and fixed point problems of nonexpansive semigroups with application to optimization problems

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Sunthrayuth P., Kumam P.

Publisher: Hindawi

Publication year: 2012

Journal: Abstract and Applied Analysis (1085-3375)

Volume number: 2012

ISSN: 1085-3375

eISSN: 1687-0409

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84858164658&doi=10.1155%2f2012%2f979870&partnerID=40&md5=099819dafe5ee52d4b4943e0f4c60320

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a general implicit iterative scheme base on viscosity approximation method with a ψ-strongly pseudocontractive mapping for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for a nonexpansive semigroup, and the set of solutions of system of variational inclusions with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. © 2012 Pongsakorn Sunthrayuth and Poom Kumam.

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