A new general iterative method for solution of a new general system of variational inclusions for nonexpansive semigroups in Banach spaces

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Kumam P., Sunthrayuth P.

Publisher: Hindawi

Publication year: 2011

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

Volume number: 2011

ISSN: 1110-757X

eISSN: 1687-0042

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-80052654820&doi=10.1155%2f2011%2f187052&partnerID=40&md5=ad35cff66935ec86018d60823e7de0d6

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given. ฉ 2011 Pongsakorn Sunthrayuth and Poom Kumam.

Keywords