随机泛函分析中可交换映象的随机不动点定理

张石生

随机泛函分析中可交换映象的随机不动点定理

张石生

四川大学数学系

计量
- 文章访问数: 1714
- HTML全文浏览量: 60
- PDF下载量: 482
- 被引次数: 0
出版历程
- 收稿日期: 1981-10-24
- 刊出日期: 1982-06-15

Random Fixed Point Theorems for Commuting Random Operators in Probabilistic Functional Analysis

Chang Shih-sen

Sichuan University, Chengdu

摘要

摘要: 随机不动点定理在随机泛函分析中是一重要问题.在可分完备的度量空间中的随机不动点定理Bharucha-Reid,王梓坤,Špa?ek,Hanš,Itoh及作者等都曾进行过讨论(见[1-5,15-20,21]).在本文中我们对概率分析中可交换映象的随机不动点定理得出了几个新的结果,它推广了前述诸人工作中某些重要结果.在确定性情形也推广了Jungck^[6,7,8],Das,Naik^[9],Rhoades^[10],及Ciric^[11]的结果.

Abstract: Random fixed point theorems are of fundamental importance in probabilistic functional analysis. In complete separable metric space random fixed point theorems have been discussed by Bharucha-Reid^[1], Hans^[3], Itoh^[4,5] and the author's papers^[15-20].In this paper we obtain a random fixed point theorem for commuting random operators in probabilistic functional analysis. Our results generalize some important results also extend and unify some results in Jungck^[6,7,8]. Das and Naiki^[9] as well as Bhoades^[10] adn ciric^[11].

HTML全文

参考文献(21)

[1]	Bharucha-Reid,A.T.,Random Integral Equation,Academic Press,New York,London,1972.
[2]	Bharucha-Reid,A.T.,Fixed point theorem in probabilistic analysis,Bull.Amer.Math.Soc.82(1976),641-657.
[3]	Hans.O.,Random fixed point theorems.in Trans.of the First Prague Conference on Information Theory,Statistical Decision Functions,Random Processes,105-125. Prague.(1957).
[4]	Itoh.S.,A random fixed point theorem for a.multivalued contraction mapping,Pacific J.Math.68(1977),85-90.
[5]	Itoh.S.,Random fixed point theorems with an application to random differential equations in Banach space,J.Math.Anal.Appl.67. No.2(1979),261-273.
[6]	Jungck.G.,Commuting mappings and fixed points,Amer,Math.Monthly 83(1976),261-263.
[7]	Jungck.F.,Periodic and Fixed points,and commuting mappings,Proc.Amer.Math.Soc.V.76,No.2(1979),333-338.
[8]	Jungck.G.,A common fixed point theorem for commuting maps on L-spaces,Math. Japonica 25. NO. 1 (1980), 81-85.
[9]	Das,K. M., and Naik. K. V., Common fixed point theorems for commuting maps on a metric space,Proc. Amer. Math. Soc. V. 77. NO. 3 (1979),369-373.
[10]	Rhoades,B. E., Comparison of various definitions of contractive mappings.Trans. Amer. Math. Soc. 226 (1977). 256-290.
[11]	Ciric. B., A generalization of Banach's contraction principle. Proc. Amer Math. Soc. v. 45,NO. 2,(1974),267-273.
[12]	Kannan,R.,and Salehi, H., Random nonlinear-equations and monotone nonlinearities, J. Math. Anal. Appl. V. 57, (1977), 234-256.
[13]	Spacek. A., Zufallige Gleichungen. Czechoslovak. Math. J. 5 (1955), 462-466.
[14]	Leader. S., Fixed points for general contractions in metric spaces. Math.Japonica 24. NO. 1 (1979), 17-24.
[15]	张石生,关于-个多值映象的不动点定理,自然杂志,6,(1981),476-477.
[16]	Chang Shih-sen. Random fixed point theorem in probabilistic analysis, Nonlinear Analysis. V. 5, NO. 2. (1981), 113-122.
[17]	张石生,关于随机映象的-个随机不动点定理,成都科技大学学报,2.(1981),73-79
[18]	张石生,关于随机分析的不动点定理(1),四川大学学报.3,(1980),9-16
[19]	张石牛.陈绍仲.随机分析中的不动点宁理及对随机逼近理论的应用.应用戮学学报,(1981)
[20]	张石生.关于多值映象序列的不动点定理,四川大学学报.4,(1980),61-68
[21]	王梓坤.随机泛函分析引论、数学进展.5.1(1962),46-71