Viscosity approximation of a common solution of fixed point, generalized equilibrium and constrained convex minimization problems

Abstract

In this paper, we introduce a viscosity iterative algorithm that approximates a common solution of constrained convex minimization problem, a generalized equilibrium problem involving averaged mapping and fixed point problem of 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.