Generalized contraction mapping

principle and differential equations

in probabilistic metric spaces

Authors:
S. S. Chang, B. S. Lee, Y. J. Cho, Y. Q. Chen, S. M. Kang and J. S. Jung

Journal:
Proc. Amer. Math. Soc. **124** (1996), 2367-2376

MSC (1991):
Primary 46S50, 34G20, 54H25

DOI:
https://doi.org/10.1090/S0002-9939-96-03289-3

MathSciNet review:
1322915

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Abstract | References | Similar Articles | Additional Information

Abstract: A new generalized contraction mapping principle in probabilistic metric spaces is obtained. As an application, we utilize this principle to prove the existence theorems of solutions to differential equations in probabilistic metric spaces. All the results presented in this paper are new.

**1.**S. S. Chang,*On the theory of probabilistic metric spaces with applications*, Z. Wahrsch. Gebiet**67**(1984), 85--94. MR**86a:54056****2.**S. S. Chang, Y. Q. Chen, and J. L. Guo,*Ekeland's variational principle and Caristi's fixed point theorem in probabilistic metric spaces*, Acta Math. Appl. Sinica**7**(1991), 217--228. MR**93b:49021****3.**S. S. Chang, Y. J. Cho, and S. M. Kang,*Probabilistic metric spaces and nonlinear operator theory*, Sichuan Univ. Press, P. R. China, 1994.**4.**B. Schweizer and A. Sklar,*Statistical metric spaces*, Pacific J. Math.**10**(1960), 313--334. MR**22:5955****5.**B. Schweizer, A. Sklar, and E. Thorp,*The metrization of statistical metric spaces*, Pacific J. Math.**10**(1960), 673--675. MR**22:5956**

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Additional Information

**S. S. Chang**

Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, People’s Republic of China

**B. S. Lee**

Affiliation:
Department of Mathematics, Kyungsung University, Pusan 608-736, Korea

Email:
bslee@ksmath.kyungsung.ac.kr

**Y. J. Cho**

Affiliation:
Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

**Y. Q. Chen**

Affiliation:
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, People’s Republic of China

**S. M. Kang**

Affiliation:
Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea

**J. S. Jung**

Affiliation:
Department of Mathematics, Dong-A University, Pusan 604-714, Korea

Email:
jungjs@seunghak.donga.ac.kr

DOI:
https://doi.org/10.1090/S0002-9939-96-03289-3

Keywords:
Generalized contraction mapping,
probabilistic metric space,
probabilistic normed space,
probabilistic bounded set

Received by editor(s):
January 3, 1995

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society