The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems

The hybrid block iterative algorithm for solving the system of equilibrium problems and variational inequality problems

ABSTRACT In this paper, we construct the hybrid block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi - ϕ- asymptotically nonexpansive mappings, the set of the solutions of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of equilibrium problems. Mor...

A New Hybrid Iterative Algorithm for Fixed-Point Problems, Variational Inequality Problems, and Mixed Equilibrium Problems

We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the variational inequality of a monotone mapping, and the set of solutions of a mixed equilibrium problem. This study, proves a strong convergence theorem by the proposed hybrid iterative algorithm which solves fixed-point ...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

An Iterative Scheme for Generalized Equilibrium, Variational Inequality and Fixed Point Problems Based on the Extragradient Method

The problem ofgeneralized equilibrium problem is very general in the different subjects .Optimization problems, variational inequalities, Nash equilibrium problem and minimax problems are as special cases of generalized equilibrium problem. The purpose of this paper is to investigate the problem of approximating a common element of the set of generalized equilibrium problem, variational inequal...

A New Iterative Scheme for Solving the Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces

We introduce the new iterative methods for finding a common solution set of monotone, Lipschitztype continuous equilibrium problems and the set of fixed point of nonexpansive mappings which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Hilbert space. The main result extends various results existing in the current...