ITERATIVE APPROXIMATIONS OF FIXED POINTS FORASYMPTOTICALLY DEMICONTRACTIVE MAPPINGS

Abstract

Let T be a completely continuous, uniformly L-Lipschitzian and asymptotically demicontractive self-mapping of a nonempty bounded closed convex subset of a Hilbert space. It is proved that, under certain conditions, the modified Ishikawa iterative sequence converges strongly to some fixed point of T. A related result deals with the iterative approximation of completely continuous, uniformly L-Lipschitzian and k-strict asymptotically pseudocontractive self-mappings in K.