The Embedded Theorem for Family of Quasi Metric Spaces in Menger Space and Its Application

Liu Zuo-shu; Zheng Quan

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Article Navigation > Applied Mathematics and Mechanics > 1990 > 11(5): 423-430

Liu Zuo-shu, Zheng Quan. The Embedded Theorem for Family of Quasi Metric Spaces in Menger Space and Its Application[J]. Applied Mathematics and Mechanics, 1990, 11(5): 423-430.

Citation:

Liu Zuo-shu, Zheng Quan. The Embedded Theorem for Family of Quasi Metric Spaces in Menger Space and Its Application[J]. Applied Mathematics and Mechanics, 1990, 11(5): 423-430.

Citation:

Liu Zuo-shu, Zheng Quan. The Embedded Theorem for Family of Quasi Metric Spaces in Menger Space and Its Application[J]. Applied Mathematics and Mechanics, 1990, 11(5): 423-430.

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The Embedded Theorem for Family of Quasi Metric Spaces in Menger Space and Its Application

Liu Zuo-shu¹,
Zheng Quan²

1.
Dept. of Math, and Physics, Wuhan University of Technology, Wuhan;
2.
Dept. of Math., Huazhong University of Science and Technology, Wuhan

Received Date: 1986-10-25
Publish Date: 1990-05-15

Abstract

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.

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References(8)

References

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[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.
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[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).