Caristi’s condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points |
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Authors: | A V Arutyunov |
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Institution: | 1.Peoples’ Friendship University of Russia,Moscow,Russia;2.Faculty of Computational Mathematics and Cybernetics,Moscow State University,Moscow,Russia |
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Abstract: | We consider a lower bounded function on a complete metric space. For this function, we obtain conditions, including Caristi’s conditions, under which this function attains its infimum. These results are applied to the study of the existence of a coincidence point of two mappings acting from one metric space to another. We consider both single-valued and set-valued mappings one of which is a covering mapping and the other is Lipschitz continuous. Special attention is paid to the study of a degenerate case that includes, in particular, generalized contraction mappings. |
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