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Title: Ishikawa iterative process for a pair of single-valued and multivalued nonexpansive mappings in Banach spaces
Authors: A. Kaewkhao
K. Sokhuma
Keywords: Mathematics
Issue Date: 1-Dec-2010
Abstract: Let E be a nonempty compact convex subset of a uniformly convex Banach space X, and let t: E → E and T: E → K C (E) be a single-valued nonexpansive mapping and a multivalued nonexpansive mapping, respectively. Assume in addition that Fix (t) ∩ Fix (T) ≠ θ and Tw = {w} for all w ε Fix (t) ∩ Fix (T). We prove that the sequence of the modified Ishikawa iteration method generated from an arbitrary x0 ε by yn = (1 -βn) xn + βn zn, xn + 1 = (1 - n) xn + an ty n, where zn Txn and {an}, {βn} are sequences of positive numbers satisfying 0 < a ≤ an, βn b < 1, converges strongly to a common fixed point of t and T; that is, there exists x ε E such that x = tx ε Tx. Copyright © 2010 K. Sokhuma and A. Kaewkhao.
ISSN: 16871812
Appears in Collections:CMUL: Journal Articles

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