General algorithm for equilibrium problems and set-valued operators


	Open access
	General algorithm for equilibrium problems and set-valued operators


	Fixed Point Theory, Volume 19, No. 1, 2018, 193-210, February 1st, 2018 DOI: 10.24193/fpt-ro.2018.1.15 Authors: Mohammad Eslamian Abstract: In this paper we introduce and study a general algorithm to approximate a common element of the set of solutions of a system of equilibrium problems and the set of common fixed points of an infinite family of quasi-nonexpansive set-valued mappings. We prove strong convergence of such algorithm in a real Hilbert space. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. Our results improve and extend many related results in the literature. Key Words and Phrases: Equilibrium problem, set-valued mapping, variational inequality, quasi-nonexpansive mapping, common fixed point. 2010 Mathematics Subject Classification: 47J25, 47N10, 65J15, 90C25, 47H10. Published on-line: February 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents