Monotone variational inequalities, generalized equilibrium problems and fixed point methods

Monotone variational inequalities, generalized equilibrium problems and fixed point methods

In this paper, we study monotone variational inequalities and generalized equilibrium problems. Weak convergence theorems are established based on a fixed point method in the framework of Hilbert spaces.

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

iterative methods for equilibrium problems, variational inequalities and fixed points

Strong Convergence for Generalized Equilibrium Problems, Fixed Point Problems and Relaxed Cocoercive Variational Inequalities

We introduce a new iterative scheme for finding the common element of the set of solutions of the generalized equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of the variational inequality problems for a relaxed u, v cocoercive and ξ-Lipschitz continuous mapping in a real Hilbert space. Then, we prove the strong convergence o...

Parallel hybrid iterative methods for variational inequalities, equilibrium problems and common fixed point problems

In this paper we propose two strongly convergent parallel hybrid iterative methods for finding a common element of the set of fixed points of a family of asymptotically quasi φ-nonexpansive mappings, the set of solutions of variational inequalities and the set of solutions of equilibrium problems in uniformly smooth and 2-uniformly convex Banach spaces. A numerical experiment is given to verify...