A viscosity hybrid steepest-descent method for a system of equilibrium and fixed point problems for an infinite family of strictly pseudo-contractive mappings

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Publication Details

Author list: Witthayarat U., Kim J.K., Kumam P.

Publisher: SpringerOpen

Publication year: 2012

Journal: Journal of Inequalities and Applications (1025-5834)

Volume number: 2012

ISSN: 1025-5834

eISSN: 1029-242X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84873339174&doi=10.1186%2f1029-242X-2012-224&partnerID=40&md5=caac7332ee3f9ad1422f54051a24d180

Languages: English-Great Britain (EN-GB)

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Abstract

Based on a viscosity hybrid steepest-descent method, in this paper, we introduce an iterative scheme for finding a common element of a system of equilibrium and fixed point problems of an infinite family of strictly pseudo-contractive mappings which solves the variational inequality [InlineEquation not available: see fulltext.] for [InlineEquation not available: see fulltext.]. Furthermore, we also prove the strong convergence theorems for the proposed iterative scheme and give a numerical example to support and illustrate our main theorem. MSC: 46C05, 47D03, 47H05,47H09, 47H10, 47H20. ฉ 2012 Witthayarat et al.; licensee Springer.

Keywords

Common fixed point, hybrid steepest-descent method