The Hybrid Steepest Descent Method for Addressing Fixed Point Problems and System of Equilibrium Problems

In this paper, we suggest and analyze an iterative scheme based on the hybrid steepest descent method for finding a common element of the set of solutions of a system of equilibrium problems, the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problems for inverse strongly monotone mappings in Hilbert spaces. We obtain a strong convergence theorem for the sequence generate by these processes in Hilbert spaces. The results in this paper improve and extend the corresponding results given by many others.