Abstract
In this paper we first introduce the concept of probabilistic interval space. Under this framework, a new version of KKM theorem is obtained. As application, we utilize this result to study some new minimax theorem, section theorem, matching theorem, coincidence theorem and fixed point theorem in probabilistic metric spaces. The results presented in this paper not only contain the main result of von Neumann[7] as its special case but also extend the corresponding results of [1, 3, 4, 6, 8] to the case of probabilistic metric spaces.
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Project supported by the National Natural Science Foundation of China
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Shisheng, Z., Cho, Y.J. & Ziang, W. New version of KKM theorem in probabilistic metric spaces with applications. Appl Math Mech 17, 1009–1019 (1996). https://doi.org/10.1007/BF00119948
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DOI: https://doi.org/10.1007/BF00119948