Fixed point solutions of variational inequalities for a semigroup of asymptotically nonexpansive mappings in Banach spaces

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

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Publication Details

Author list: Sunthrayuth P., Kumam P.

Publisher: SpringerOpen

Publication year: 2012

Journal: Fixed Point Theory and Applications (1687-1820)

Volume number: 2012

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84879631694&doi=10.1186%2f1687-1812-2012-177&partnerID=40&md5=582b1dec6c3a7e7ce17ad8200e293695

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this article is to introduce two iterative algorithms for finding a common fixed point of a semigroup of asymptotically nonexpansive mappings which is a unique solution of some variational inequality. We provide two algorithms, one implicit and another explicit, from which strong convergence theorems are obtained in a uniformly convex Banach space, which admits a weakly continuous duality mapping. The results in this article improve and extend the recent ones announced by Li et al. (Nonlinear Anal. 70:3065-3071, 2009), Zegeye et al. (Math. Comput. Model. 54:2077-2086, 2011) and many others. ฉ 2012 Sunthrayuth and Kumam; licensee Springer.

Keywords

Iterative approximation method, Semigroup of asymptotically nonexpansive mapping, Uniformly convex Banach space