Abstract
The purpose of this paper is to introduce and study the semi-groups 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, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.
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Project supported by the National Natural Science Foundation of China
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Shisheng, Z., Yuqing, C. Nonlinear semigroups and differential inclusions in probabilistic normed spaces. Appl Math Mech 19, 815–829 (1998). https://doi.org/10.1007/BF02458236
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DOI: https://doi.org/10.1007/BF02458236