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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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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: http://dx.doi.org/10.1090/S0002-9939-96-03289-3
PII: S 0002-9939(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