Weak and strong convergence of the Ishikawa iterative sequence to fixed points of Lipschitz pseudocontractive maps in Hilbert spaces

Abstract

In this paper, we study the weak and strong convergence of the Ishikawa iterative sequence to a fixed point of a Lipschitz pseudocontrative mapping in a Hilbert space. We do not require any compactness type assumptions either on the mapping or its domain. Furthermore, we do not need to compute for closed convex subsets, Cn, of the Hilbert space.