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In this paper, we consider a two-person zero-sum differential game with incomplete information on the initial state, namely, the first player has a private information while the second player knows only a probability distribution on the initial state, and obtain the existence of its value functions. The main novelty lies in the method for which we apply a generalized weak contraction for dynamic systems and terminal cost functions instead of the Lipschitz contractive condition on a partially ordered metric space. [ABSTRACT FROM AUTHOR]

In this paper, hybrid best proximity points for a class of proximally mixed monotone set-valued mappings are discussed. In order to get rid of the fetter of continuity, we introduce the proximally ordered contraction instead of various proximal distance contractions widely applied in recent literatures and present some new existence and iterative approximation theorems of best proximity points for such mappings. Some examples are given to illustrate the advantages of the obtained results. [ABSTRACT FROM AUTHOR]