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Some notes on Ishikawa iteration for multi-valued mappings. (English) Zbl 1218.47120
Summary: N. Shahzad and H. Zegeye [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 3–4, A, 838–844 (2009; Zbl 1218.47118)] introduced several Ishikawa iterative schemes for fixed points of multi-valued mappings in Banach spaces and proved some strong convergence theorems for them. In their proofs, it seems reasonable and simpler to prove for the iteration {x n } to be a Cauchy sequence. In the present paper, we thus modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.
47J25Iterative procedures (nonlinear operator equations)
47H04Set-valued operators
47H09Mappings defined by “shrinking” properties