Abstract
In this paper, a monotone variational inequality, a system of equilibrium problems, and nonexpansive mappings are investigated based on an iterative algorithm. Weak convergence theorems of common solutions are established in Hilbert spaces.
Highlights
Equilibrium problems which were introduced by Blum and Oettli [ ] have intensively been studied
It has been shown that equilibrium problems cover fixed point problems, variational inequality problems, inclusion problems, saddle problems, complementarity problem, minimization problem, and Nash equilibrium problem; see [ – ] and the references therein
Equilibrium problem has emerged as an effective and powerful tool for studying a wide class of problems which arise in economics, finance, image reconstruction, ecology, transportation, network, elasticity, and optimization; see [ – ] and the references therein
Summary
Equilibrium problems which were introduced by Blum and Oettli [ ] have intensively been studied. A monotone variational inequality, a system of equilibrium problems, and nonexpansive mappings are investigated based on an iterative algorithm.
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