WEAK AND STRONG CONVERGENCE OF AN ITERATIVE ALGORITHM FOR LIPSCHITZ PSEUDO-CONTRACTIVE MAPS IN HILBERT SPACE

WEAK AND STRONG CONVERGENCE OF AN ITERATIVE ALGORITHM FOR LIPSCHITZ PSEUDO-CONTRACTIVE MAPS IN HILBERT SPACE

ABSTRACT

Let H be a real Hilbert space and K a nonempty, closed convex subset of H.Let Tn: K → K be Lipschitz pseudo-contractive map with a nonempty fixed points set. We introduce a modified Ishikawa iterative algorithm for Lipschitz pseudo-contractive maps and prove that our new iterative algorithm converges strongly to a fixed point of T in real Hilbert space.