复合g-收缩映射不动点定理及其应用

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

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

摘要: 任一几何平均收缩比率小于1(简称g-收缩映射)的由完备的非空度量空间M到M的复合序列映射,复合周期映射有在M中的唯一的不动点。文中给出定理应用于一组非线性微分方程以及扁壳轴对称弯曲的耦合的积分方程的解的存在和唯一性证明的应用例子。
- 收缩映射 /
- g-收缩映射 /
- Banach收缩映射定理 /
- 泛函分析 /
- 迭代法 /
- 微分方程 /
- 积分方程 /
- 扁壳
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 /

[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.