APPROXIMATING FIXED POINTS OF LIPSCHITZ PSEUDO-CONTRACTIVE SEMIGROUPS AND SOLUTIONS OF VARIATIONAL INEQUALITIES

Abstract

Let C be a closed and convex subset of a real Hilbert space H, T be a pseudo- contractive semigroup on C and A be a Lipschitz monotone mapping from C into H. In this paper, we propose and investigate an iterative scheme for finding a common element of the set of common fixed points of T and the set of solutions of the variational inequality V I(A, C). As a consequence, we prove that the scheme generated by the new method converges strongly under mild conditions on the parameters involved.