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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Original Russian Text © A.V. Arutyunov, 2015, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Vol. 291, pp. 30–44.
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Arutyunov, A.V. Caristi’s condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points. Proc. Steklov Inst. Math. 291, 24–37 (2015). https://doi.org/10.1134/S0081543815080039
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DOI: https://doi.org/10.1134/S0081543815080039