Hierarchical equilibrium and generalized variational inequality problems

Abstract

In this paper, we study the convex feasibility problem (CFP) in the case that each is a solution set of the generalized variational inequality and the equilibrium problem and introduce a new approach method to find a common element in the intersection of the set of the solutions of a finite family of equilibrium problems and the intersection of the set of the solutions of a finite family of generalized variational inequality problems in a real Hilbert space which is a unique solution of the hierarchical equilibrium and generalized variational inequality problems(HEGVIP). Under appropriate conditions, some strong convergence theorems are established. Our results generalize and improve the corresponding results of Wairojjana and Kumam (2013) [27] and some authors. © 2014 Springer Science+Business Media Dordrecht.