凸距离空间内星形子集非扩张型映射不动点*
Fixed Points of Nonexpansive Mappings on Star-Shaped Subsets of a Convex Metric Space
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摘要: 在本文中.我们给出包含一个集合的某种星形集的刻划及其性质.然后利用这些刻划和性质讨论凸距离空间的星形子集上非扩张型映射的不动点的存在问题,推广了丁协平、Beg和Azam的某些最近结果.最后还给出一个例子说明以上推广是本质上的推广.Abstract: In this paper,we give some characteristic properties of star-shaped sets which include a subset of a convex metric space.Using the characteristic properties,we discuss the ezistence problems of fized points of nonezpansive type mappings on star-shaped subsets of convex metric spaces, which generalize the recent results obtained by Ding Xie-ping, Beg and Azam. Finally, we give an ezample which shows that our generalizations are essential.
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Key words:
- star-shaped set /
- star centre /
- nor mal structure of a star-shaped set
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[1] Takahashi,W.,A convexity in metric space and noneapansive mappings,I,Kodai Math.Sum,Rep,,22(1970),142-149. [2] 丁协平,T-凸距离空间内非扩张型映射的不动点,纯粹数学与应用数学,5(1989),39-42. [3] Beg,Ismat and Akbar Azam,Fixed points on star-shaped subsets of convey metric spaces.Indian J.Pure Appl.Moth.,18(7)(1987),594-596. [4] 张石生、黄发伦,关于Banach空间中平均非扩张映象的不动点理论,四川大学学报(自然科学版),(2)(1975),67-78. [5] Jaggi,D.S.,On fiacd points of noneapansive mappings,Contemporary Mathe maticaly(1983),147-149. [6] Wong,C,S.,On Kannan maps,Proc,Amer,Math.Soc,,(47)(1975),105-111. [7] Kannan,R,,Fized point theorems in reflexive Banach spaces,Proc.Amer.Math.Soc,,(38)(1973),111-118. -
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