A New Iterative Scheme for Countable Families of Weak Relatively Nonexpansive Mappings and System of Generalized Mixed Equilibrium Problems

We construct a new iterative scheme by hybrid methods and prove strong convergence theorem for approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a solution to a system of generalized mixed equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth using the properties of generalized f-projection operator. Using this result, we discuss strong convergence theorem concerning general H-monotone mappings and system of generalized mixed equilibrium problems in Banach spaces. Our results extend many known recent results in the literature

STRONG CONVERGENCE THEOREMS FOR VARIATIONAL INEQUALITY PROBLEMS AND SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS

Abstract. In this paper, we construct a new iterative scheme by hybrid method for approximation of common element of set of solutions of a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the two sets. We give several applications of our results in a Banach space. Our results extend many important recent results in the literature

A General Composite Algorithms for Solving General Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

We introduce a general composite algorithm for finding a common element of the set of solutions of a general equilibrium problem and the common fixed point set of a finite family of asymptotically nonexpansive mappings in the framework of Hilbert spaces. Strong convergence of such iterative scheme is obtained which solving some variational inequalities for a strongly monotone and strictly pseudocontractive mapping. Our results extend the corresponding recent results of Yao and Liou (2010)

Some recent advances in projection-type methods for variational inequalities

AbstractProjection-type methods are a class of simple methods for solving variational inequalities, especially for complementarity problems. In this paper we review and summarize recent developments in this class of methods, and focus mainly on some new trends in projection-type methods