Fixed Point Theorem of Composition g-Contraction Mapping and Its Applications

YUN Tian-quan

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YUN Tian-quan. Fixed Point Theorem of Composition g-Contraction Mapping and Its Applications[J]. Applied Mathematics and Mechanics, 2001, (10): 1022-1028.

Citation:

YUN Tian-quan. Fixed Point Theorem of Composition g-Contraction Mapping and Its Applications[J]. Applied Mathematics and Mechanics, 2001, (10): 1022-1028.

Citation:

YUN Tian-quan. Fixed Point Theorem of Composition g-Contraction Mapping and Its Applications[J]. Applied Mathematics and Mechanics, 2001, (10): 1022-1028.

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Fixed Point Theorem of Composition g-Contraction Mapping and Its Applications

YUN Tian-quan

Department of Mechanics, South China University of Technology, Guangzhou 510641, P R China

Received Date: 2000-05-26
Rev Recd Date: 2001-05-16
Publish Date: 2001-10-15

Abstract

Abstract

Any composition sequential mapping,periodic composition mapping of a complete nonempty metric space M into M with geometric mean contraction ratio less than 1(simplifying as"g-contraction mapping") has a unique fixed point in M .Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.
- contraction mapping,
- g-contraction mapping,
- Banach contraction mapping theorem,
- functional analysis,
- differential equation,
- integral equation,
- shallow shell,

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References(8)

References

[1]	Rhoades B E.A comparison of various definitions of contractive mappings[J].Transactions of the Amer Math Soc,1977,226(2):257-290.
[2]	LOU Ben-dong.Fixed points for operators in a space of continuous functions and applications[J].Proceedings of Amer Math Soc,1999,127(8):2259-2264.
[3]	Smart D R.Fixed Point Theorems[M].Brooke Crutchley:Cambridge Univ Press,1974,78-79.
[4]	Cronin J.Differential Equations,Introduction and Qualitative Theory[M].New York:Marcel Dekker Inc,1980,74-76.
[5]	夏道行,吴卓人,严绍宗,等.实变函数论与泛函分析,下册[M].北京:人民教育出版社,1979:74-77.
[6]	云天铨.积分方程及其在力学中的应用[M].广州:华南理工大学出版社,1990,389-396.
[7]	Keller H B,Reiss E L.Iterative solutions for the non-linear bending of circular plates[J].Comm Pure Appl Math,1958,9:273-292.
[8]	Reissner E.Symmetric bending of shallow shells of revolution[J].J Math Mech,1958,7(2):121-140.