journal6 ›› 2003, Vol. 24 ›› Issue (2): 35-38.

• 数学 • 上一篇    下一篇

关于拟度量族生成空间上的不动点定理

  

  1. (盐城师范学院数学系,江苏 盐城224002)
  • 出版日期:2003-06-15 发布日期:2012-11-07

On Fixed Point Theorems in Generating Spaces of Quasi-metric Family

  1. (Dept.of Math.,Yancheng Teachers College,Yancheng 224002,Jiangsu China)
  • Online:2003-06-15 Published:2012-11-07
  • About author:XIAO Jian-zhong(1958-),male,was born in Taixing county,professor,of the Dept. of Math. Yancheng Teachers College.
  • Supported by:

    Supported by the Natural Science Foundation of the Education Committee of Jiangsu Province(02KJD110007)

摘要:在拟度量族生成空间上引入广义局部幂压缩映射的定义,讨论了映射轨道的有界性与迭代序列的收敛性,利用这些性质,建立了有关拟度量族生成空间上广义局部幂压缩映射的几个不动点定理.这些定理不仅推广与统一了通常度量空间与Menger概率度量空间的相应结果,而且也包含了Kaleva-Seikkala模糊度量空间中压缩型映射的不动点定理作为其特殊情形.

关键词: 拟度量族, 广义局部幂压缩映射, 轨道, 迭代序列, 不动点, 模糊度量空间, 概率度量空间

Abstract: The concept of a generalized local power contractive mapping is introduced in generating spaces of quasi-metric family.The boundedness of mapping orbit and the convergence of iterative sequence are discussed.By means of these properties,some fixed point theorems for generalized local power contractive mapping are established in generating spaces of quasi-metric family.These results not only unify and extend the corresponding results of usual metric spaces and Menger probabilistic metric spaces,but also contain the fixed point theorems for contraction type mappings in Kaleva-Seikkala fuzzy metric spaces as their special cases.

Key words: quasi-metric family, generalized local power contractive mapping, orbit, iterative sequence, fixed point, fuzzy metric space, probabilistic metric space

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