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Generalized contraction mapping principle and differential equations in probabilistic metric spaces |
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| Authors: | S S Chang B S Lee Y J Cho Y Q Chen S M Kang J S Jung |
| Institution: | Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, People's Republic of China B. S. Lee ; Department of Mathematics, Kyungsung University, Pusan 608-736, Korea ; Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea Y. Q. Chen ; Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, People's Republic of China S. M. Kang ; Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea J. S. Jung ; Department of Mathematics, Dong-A University, Pusan 604-714, Korea |
| 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. |
| Keywords: | Generalized contraction mapping probabilistic metric space probabilistic normed space probabilistic bounded set |
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