Caristi’s Inequality and α-Contraction Mappings
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A new Caristi-type inequality is considered and Caristi’s fixed point theorem for mappings of complete metric spaces is developed (in both the single- and set-valued cases). On the basis of this development mappings of complete metric spaces which are contractions with respect to a function of two vector arguments are studied. This function is not required to be a metric or even a continuous function. The proved theorems are generalizations of the Banach contraction principle and Nadler’s theorem.
Key wordsfixed point set-valued mapping metric space contraction mapping
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This work was supported by the Russian Science Foundation (project no. 19-01-00080).
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