The modified viscosity implicit rules for variational inequality problems and fixed point problems of nonexpansive mappings in Hilbert spaces

Abstract

The purpose of this paper is to introduce a modified viscosity implicit rules for finding a common element of the set of solutions of variational inequality problems for two inverse-strongly monotone operators and the set of fixed points of one nonexpansive mapping in Hilbert spaces. Under some suitable assumptions imposed on the parameters, we obtain some strong convergence theorems. We also apply our main results to solve fixed point problems for strict pseudocontractive mappings and equilibrium problems in Hilbert spaces. A numerical example is given for supporting our main results.