AN ITERATIVE ALGORITHM FOR GENERALISED MIXED EQUILIBRIUM PROBLEMS, VARIATIONAL INEQUALITY PROBLEMS AND OPTIMISATION PROBLEMS

Abstract

In this paper, we consider a general composite iterative algorithm for finding a common element of the set of solutions of a generalised mixed equilibrium problem, the set of fixed points of an infinite family of non-expansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions, which solves a certain optimisation problem. The results of this article substantially improve, develop, and complement the previous well-known results in this area.