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锥度量空间中Lipschitz型映射的公共不动点定理 被引量:32

Common Fixed Point Theorem of Lipschitz Type Mappings on Cone Metric Space
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摘要 本文在锥度量空间框架下,证明了几个满足Lipschitz型条件的映射对的公共不动点定理,其结果是许多压缩型不动点定理的推广,并举例说明本文定理是通常压缩型不动点定理的真推广. In this paper,some common fixed points of a pair of self mappings satisfying a Lipschitz type conditions in cone metric space or metric space are proven.The results are more general than the known fixed point theorem of contractive type mappings. Some examples are given,which show that the mappings satisfy the conditions in this paper but cannot satisfy the general contractive type conditions.
作者 张宪
机构地区 集美大学理学院
出处 《数学学报(中文版)》 SCIE CSCD 北大核心 2010年第6期1139-1148,共10页 Acta Mathematica Sinica:Chinese Series
关键词 公共不动点 Lipschitz型映射 锥度量空间 common fixed point Lipschitz type condition cone metric space
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  • 1Huang, L. G., Zhang, X.: Cone metric spaces and fixed point theorems of contractive mappings. Y. Math. Anal. App., 332, 1468-1476 (2007).
  • 2Ilic, D., Rakocevic, V.: Common fixed points for maps on cone metric space. J. Math. Anal. Appl., 341(2), 876-882 (2008).
  • 3Abbas, M., Jungck, G.: Common fixed point results for noncommuting mappings without continuity in cone metric spaces. J. Math. Anal. Appl., 341(1), 416-420 (2008).
  • 4Xu, H. K.: Diametrically contractive mappings. Bulletin of the Australian Mathematical Society, 70(3), 463-468 (2004).
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共引文献9

同被引文献106

  • 1何松年.第Ⅱ、Ⅲ型膨胀映射的不动点定理[J].中国民航学院学报,2004,22(5):50-51. 被引量:8
  • 2张宪.序压缩映射的不动点定理[J].数学学报(中文版),2005,48(5):973-978. 被引量:40
  • 3朴勇杰.2-度量空间上具有唯一公共不动点的拟收缩型非交换自映射族[J].黑龙江大学自然科学学报,2006,23(5):655-657. 被引量:10
  • 4何松年.弱膨胀映射及其不动点定理[J].南京大学学报(数学半年刊),2006,23(2):334-340. 被引量:6
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  • 6朱辅正.关于若干扩张映象的不动点定理.江西师范大学学报:自然科学版,1988,:28-34.
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  • 9Abbas M, Rhoades B E. Fixed and periodic point results in cone metric spaces [ J ]. Applied Mathematics Letters, 2009,22(4) :511-515.
  • 10Ishak A, Gonca D. Some fixed point theorems on ordered cone metric spaces[ J]. Rendiconti Del Circolo Matematico Di Palermo,2009,58(2) :319-325.

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