Implicit iterative methods for nonexpansive mappings and monotone mappings

Abstract

In this paper, we study some implicit algorithms to approximate a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an inverse strongly monotone mapping in Hilbert spaces. Using shrinking projection method, we obtain couple of strong convergence results. As applications of our results a new algorithm is derived to find a common fixed point of two mappings. We also suggest an algorithm to approximate solution of split feasibility problem.