Weak and strong convergence theorems without some widely used conditions

Abstract

We establish weak (strong) convergence of Ishikawa iterates of two asymptotically (quasi-)nonexpansive maps without any condition on the rate of convergence associated with the two maps. Moreover, our weak convergence results do not require any of the Opial condition, Kadec-Klee property or Fr�chet differentiable norm. ? 2010 Academic Publications.