Abstract
We present an operator inequality of a new type which yields the existence of a minimum point for a (non necessarily continuous) function on a complete metric space. The estimation of proximity of the minimum point to a given point of the space is produced. The obtained theorem is applied to the proofs of new theorems on fixed and coincidence points for single-valued and multivalued maps in complete metric spaces. In all cases the localization of these points is also given.
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Funding
Results of V.V. Obukhovskii were obtained under support of Russian Science Foundation (project no. 22-71-10008).
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Dedicated to the memory of Professor Ivan Alexandrovich Kipriyanov
(Submitted by A. B. Muravnik)
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Gel’man, B., Obukhovskii, V. & Borisova, E. Some Theorems on a Minimum of a Function, Fixed and Coincidence Points. Lobachevskii J Math 44, 3292–3297 (2023). https://doi.org/10.1134/S1995080223080164
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DOI: https://doi.org/10.1134/S1995080223080164