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

Chang Shih-sen

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Chang Shih-sen. Random Fixed Point Theorems for Commuting Random Operators in Probabilistic Functional Analysis[J]. Applied Mathematics and Mechanics, 1982, 3(3): 345-354.

Citation:

Chang Shih-sen. Random Fixed Point Theorems for Commuting Random Operators in Probabilistic Functional Analysis[J]. Applied Mathematics and Mechanics, 1982, 3(3): 345-354.

Citation:

Chang Shih-sen. Random Fixed Point Theorems for Commuting Random Operators in Probabilistic Functional Analysis[J]. Applied Mathematics and Mechanics, 1982, 3(3): 345-354.

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

Chang Shih-sen

Sichuan University, Chengdu

Received Date: 1981-10-24
Publish Date: 1982-06-15

Abstract

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].

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References(21)

References

[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