Iterative methods for variational inequality problems and fixed point problems of a countable family of strict pseudo-contractions in a q-uniformly smooth Banach space

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-s2.0-84869009206&doi=10.1186%2f1687-1812-2012-65&partnerID=40&md5=57e396829ebe2e9a7a53076e5cab80bf

Languages: English-Great Britain (EN-GB)

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Abstract

In this article, we introduce iterative methods (implicit and explicit) for finding a common fixed point set of a countable family of strict pseudo-contractions, which is a unique solution of some variational inequality. Furthermore, we prove the strong convergence theorems of such iterative scheme in a q-uniformly smooth Banach space which admits a weakly sequentially continuous generalized duality mapping. The results presented in this article extend and generalize the corresponding results announced by Yamada and Ceng et al. from Hilbert spaces to Banach spaces. ฉ 2012 Sunthrayuth and Kumam; licensee Springer.

Keywords

Q-uniformly smooth Banach space, Strict pseudo-contractions