Open Access Research

Strong convergence theorems for equilibrium problems and fixed point problem of multivalued nonexpansive mappings via hybrid projection method

Ali Abkar1 and Mohammad Eslamian2*

Author Affiliations

1 Department of Mathematics, Imam Khomeini International University, Qazvin, 34149, Iran

2 Young Researchers Club, Babol Branch, Islamic Azad University, Babol, Iran

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Journal of Inequalities and Applications 2012, 2012:164 doi:10.1186/1029-242X-2012-164

Published: 23 July 2012

Abstract

In this paper, a new iterative process by the hybrid projection method is constructed. Strong convergence of the iterative process to a common element of the set of common fixed points of a finite family of generalized nonexpansive multivalued mappings and the solution set of two equilibrium problems in a Hilbert space is proved. Our results extend some important recent results.

MSC: 47H10, 47H09.

Keywords:
equilibrium problem; hybrid projection method; strong convergence; common fixed point; generalized nonexpansive multivalued mapping