A common solution of constrained convex minimization problem, generalized equilibrium problem and fixed point problem of directed nonexpansive mappings

Abstract

In this paper, we introduce an iterative algorithm that approximates a common solution of a constrained minimization problem of convex function, a generalized equilibrium problem involving averaged mapping, and fixed point problem of a directed nonexpansive mapping. We prove the strong convergence of the proposed iterative algorithm to a common solution that satisfies a variational inequality under some suitable conditions on the parameters. It generalizes the familiar gradient-projection algorithm for convex minimization problem. This result improves and extends some recent results in the literature.