Probabilistic Contractor Couple and Solutions for a System of Nonlinear Equations in Non-Archimedean Menger Probabilistic Normed Spaces

Zhang Shi-sheng; Peng Yong-cheng

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Article Navigation > Applied Mathematics and Mechanics > 1991 > 12(11): 965-972

Zhang Shi-sheng, Peng Yong-cheng. Probabilistic Contractor Couple and Solutions for a System of Nonlinear Equations in Non-Archimedean Menger Probabilistic Normed Spaces[J]. Applied Mathematics and Mechanics, 1991, 12(11): 965-972.

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Probabilistic Contractor Couple and Solutions for a System of Nonlinear Equations in Non-Archimedean Menger Probabilistic Normed Spaces

Zhang Shi-sheng¹,
Peng Yong-cheng²

1.
Department of Mathematics, Sichuan Universty, Chengdu;
2.
Department of Mathematics, Shaoguan University, Guangdong

Received Date: 1990-09-27
Publish Date: 1991-11-15

Abstract

Abstract

The purpose of this paper is to introduce the concept of probabilistic contractor couple in non-Archimedean probabilistic normed spaces and to study the existencc and uniqueness of solutions for a system of nonlinear operator equations with probabilistic contractor couples in non-Archimedean probabilistic normed spaces. The results presented in this paper improve and extend the corresponding results in [1-5].
- non-Archimedean probabilistic normed space,
- probabilistic contractor couple,
- selection function,
- system of nonlinear equations

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References(7)

References

[1]	Altman,M.,Contractors and Contractor Directions,Theory and Applications,Marcel Dekker,New York(1977).
[2]	Lee,A.C.,and W.J.Padgett,Random contractors with random nonlinear majorant functions,Nonlinear Anal.TMA,3(1979),707-715.
[3]	Lee,A.C.and W.J.Padgett,Solutions of random operator equations by random step-contractors,Nonlinear Anal.TMA,4(1980),145-151.
[4]	Lee,A.C.and W.J.Padgett,Random contractors and the solution of random nonlinear equations,Nonlinear Anal.TMA,1(1977),173-185.
[5]	张石生,概率收缩和概率赋范空间中非线性方程的解,科学通报,15 (1990).
[6]	张石生,《不动点理论及应用》.重庆出版社(1984).
[7]	Schweizer,B.and A.Sklar,Probabilistic Metric Spaces,North-Holland(1983).