Iterative approximation of common solution of three classes of nonlinear problems

Abstract

We introduce an iterative algorithm and prove that the sequence of the algorithm strongly converges to a common element of the set of fixed points of asymptotically nonexpansive mapping, the set of solutions of generalized mixed equilibrium problem and the set of solutions of variational inequality problem in a real Hilbert space. Furthermore, we applied the result obtained to solve an optimization problem.