Open Access Research

A hybrid projection method for solving a common solution of a system of equilibrium problems and fixed point problems for asymptotically strict pseudocontractions in the intermediate sense in Hilbert spaces

Chatchawan Watchararuangwit1, Pongrus Phuangphoo1,2 and Poom Kumam1*

Author Affiliations

1 Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Kru, Bangkok, 10140, Thailand

2 Department of Mathematics, Faculty of Education, Bansomdejchaopraya Rajabhat University (BSRU), Thonburi, Bangkok, 10600, Thailand

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Journal of Inequalities and Applications 2012, 2012:252 doi:10.1186/1029-242X-2012-252

Published: 30 October 2012

Abstract

In this paper, we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding a common solution of a system of equilibrium problems of bifunctions satisfying certain conditions and a common solution of fixed point problems of a family of uniformly Lipschitz continuous and asymptotically <a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/252/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/252/mathml/M1">View MathML</a>-strict pseudocontractive mappings in the intermediate sense. We prove the strong convergence theorem for a new iterative algorithm under some mild conditions in Hilbert spaces. Finally, we also give a numerical example which supports our results.

MSC: 47H05, 47H09, 47H10.

Keywords:
asymptotically strict pseudocontraction in the intermediate sense; hybrid projection method; system of equilibrium problems; fixed point problems