Some notes on ishikawa iteration for multi-valued mappings

Abstract

In Shahzad and Zegeye [Nonlinear Anal. 71 (2009), no. 3-4, 838{844], the authors introduced several Ishikawa iterative schemes for xed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration {xn} to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given. © 2011 The Korean Mathematical Society.