| ON REICH'S OPEN QUESTION |
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| 作者姓名： | 张石生 |
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| 作者单位： | Department of |
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| 摘 要： | 1 IntroductionandPreliminariesThroughoutthispaperweassumethatEisarealBanachspace ,E isthedualspaceofE ,DisanonemptysubsetofEandJ:E → 2 E isthenormalizeddualitymappingdefinedbyJ(x) =f∈E , 〈x ,f〉 =‖x‖‖f‖ , ‖x‖ =‖f‖ (x∈E) . (1 ) Definition 1 LetT :D →Dbeamapping .1 .Tissaidtobeasymptoticallynonexpansive1],ifthereexistsasequence kn 1 ,∞ )withlimn→∞kn =1suchthat‖Tnx-Tny‖ ≤kn‖x-y‖ forall x ,y∈D ,n≥ 1 ; 2 .Tissaidtobenonexpansive,ifthesequence kn app…
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| 收稿时间： | 17 January 2002 |
On reich's open question |
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| Zhang Shi-sheng.ON REICH''''S OPEN QUESTION[J].Applied Mathematics and Mechanics(English Edition),2003,24(6):646-653. |
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| Authors: | Zhang Shi-sheng |
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| Institution: | Department of Mathematics, Yibin University, Yibin, Sichuan 644007, P.R.China; Department of Mathematics, Sichuan University, Chengdu 610064, P.R.China) |
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| Abstract: | Under more general form and more general conditions an affirmative answer to Reich's open question is given. The results presented also extend and improve some recent results of Reich, Shioji, Takahashi and Wittmann. |
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| Keywords: | asymptotically nonexpansive mapping nonexpansive mapping fixed point iterative approximation |
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