Convergence of the Ishikawa Iteration Process for Nonexpansive Mappings in Hyperspace

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Title:	Convergence of the Ishikawa Iteration Process for Nonexpansive Mappings in Hyperspace 超空間上非擴張函數的石川氏迭代收歛定理
Authors:	王永成(Weng-Seng Heng)
Contributors:	理學院
Keywords:	石川氏迭代非擴張函數 Hausdorff距離超空間 Ishikawa Iteration Nonexpansive Mappings Hausdorff Metric Hyperspace
Date:	2003
Issue Date:	2012-05-14 11:17:04 (UTC+8)
Abstract:	設X為賦距線性空間，KC(X)為X上所有非空緊緻的凸子集所成的集合，而א為KC(X).的子集，且T:א→KC(X)為非擴張映射。設{Xn}為א上的序列且{tn}為實序列，滿足下列： (i)運算式略 (ii)運算式略若{Xn}為有異，則limh(TXn,Xn)=0. 上述定理推廣了石川氏的結果。 Let X be a metric linear space, KC(X) is the collection of all nonempty, compact, convex subsets of X and א be a subset of KC(X). Suppose that T:א→KC(X) be a noncxpansive mapping. Given a sequence [Xn] in א and a recl scquences {tn} satisfying (i) 運算式略 (ii)運算式略 If {Xn} is bounded then lim h(THn, Xn)=0. The theorem generalize the result obtained by Ishikawa.
Relation:	華岡理科學報； 20 期 (2003 / 05 / 01) ， P175 - 182
Appears in Collections:	[College of Science] Hwa Kang Journal of Sciences

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