Some notes on Ishikawa iteration for multi-valued mappings
Bull. Korean Math. Soc. 2011 Vol. 48, No. 3, 575-584
Published online May 1, 2011
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
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