Menger空间对拟距离空间族的嵌入定理及其应用
The Embedded Theorem for Family of Quasi Metric Spaces in Menger Space and Its Application
-
摘要: 在本文中,我们引进了Menger空间中拟距离空间族的嵌入概念并研究了它的一些性质.证明了Menger空间中连续映象序列的一个公共不动点定理.这些映象是假设满足广义的压缩条件的.这里采用的证明方法对于Menger空间的映象而言是一种新的思想.Abstract: In this paper the notion of embedding for family of quasi metric spaces in Menger spaces is introduced and its properties are investigated. A common fixed point theorem for sequence of continuous mappings in Menger spaces is proved. These mappings are assumed to satisfy some generalizations of the contraction condition. The proving technique herein seems to be new even for mappings in Menger spaces.
-
[1] Menger,K.,Statistical metric,Proc.Nat.Acad.Sci.U.S.A.,28(1942),535-537. [2] Wald,A.,On a statistical generalization of metric spaces,Proc.Nat.Acad.Sci.U.S.A.,29(1943),196-197. [3] Schweizer,B.and A.Sklar,Statistical metric spaces,Pacific J.Math.,10(1960),313-334. [4] Egbert,R.T.,Products and quotients of probabilistic metric spaces,Pacific J.Math.,24(1968),437-455. [5] Schweizer,B.and A.Sklar,Probabilistic Metric Spaces,North-Holland Publisher(1983). [6] Zhu Lin-hu,Fixed point of probabilistic normal spaces and probabilistic inner product spaces,Ph.D.Dissertation,Xi'an Jiaotong University,China(1981). [7] Liu Zuo-shu,The nonlinear abstract contraction.principle and its application to statistical metric spaces,Acta.Math.Sci.,4(1984),69-79. [8] Zhang Shi-sheng,Fixed Point Theory and Application,Chongqing Press(1984). -
点击查看大图
计量
- 文章访问数: 1862
- HTML全文浏览量: 88
- PDF下载量: 540
- 被引次数: 0
下载:
