East Asian mathematical journal
- Volume 14 Issue 1
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- Pages.77-98
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- 1998
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- 1226-6973(pISSN)
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- 2287-2833(eISSN)
NONLINEAR SEMIGROUPS AND DIFFERENTIAL INCLUSIONS IN PROBABILISTIC NORMED SPACES
- Chang, S.S. (Department of Mathematics Sichuan University) ;
- Ha, K.S. (Department of Mathematics Pusan National University) ;
- Cho, Y.J. (Department of Mathematics Gyeongsang National University) ;
- Lee, B.S. (Department of Mathematics Kyungsung University) ;
- Chen, Y.Q. (Department of Mathematics Sichuan University, China)
- Published : 1998.06.25
Abstract
The purpose of this paper is to introduce and study the semigroups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, we utilize these results to study the Cauchy problem for a kind of differential inclusions with accertive mappings in probabilistic normed spaces.
Keywords
- Semigroup of nonlinear contractions;
- probabilistic normed space;
- Crandall-Liggett's exponential formula;
- semi-inner product and accretive mappings