Fixed Points Approximation and Solutions of Some Equilibrium and Variational Inequalities Problems

We prove a new strong convergence theorem for an element in the intersection of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of some variational inequality problems, and the set of solutions of some equilibrium problems using a new iterative scheme. Our theorem generalizes and improves some recent results

Approximating a common solution of a finite family of generalized equilibrium and fixed point problems

In this paper, we introduce and investigate an iterative scheme for finding a common element of the set of common solutions of a finite family of generalized equilibrium problems and the set of fixed points of a Lipschitz and hemicontractive-type multi-valued mapping. We obtain strong convergence theorems of the proposed iterative process in real Hilbert space settings. Our results improve, generalize and extend most of the recent results that have been proved by many authors in this research area