Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2011; 48(3): 575-584

Printed May 1, 2011

https://doi.org/10.4134/BKMS.2011.48.3.575

Copyright © The Korean Mathematical Society.

Some notes on Ishikawa iteration for multi-valued mappings

Yisheng Song and Yeol Je Cho

Henan Normal University, Gyeongsang National University

Abstract

In Shahzad and Zegeye [Nonlinear Anal. $\bf 71$ (2009), no. 3-4, 838--844], the authors introduced several Ishikawa iterative schemes for fixed 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 $\{x_n\}$ 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.

Keywords: multi-valued mapping, strong convergence, Ishikawa iteration

MSC numbers: 47H09, 47H10, 47J25, 47J05