ON THE STABILITY OF ITERATIVE APPROXIMATIONS OF INVERSE-STRONGLY MONOTONE MAPPING

Abstract

In this paper, we study iterative approximations for finding a common element of the fixed points of a nonexpansive mapping and the set of solutions of the variational inequalities for an inverse-strongly monotone mappings in Hilbert spaces. The conditons which guarantee strong convergence and stability of these approximations with respect to perturbations of nonexpansive operator S, metric projection operator P­ and constraint set ­ are considered. We show that the sequence converges strongly to a common element of two sets.