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Caristi’s Inequality and α-Contraction Mappings

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Functional Analysis and Its Applications Aims and scope

Abstract

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.

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Funding

This work was supported by the Russian Science Foundation (project no. 19-01-00080).

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Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    B. D. Gel’man

  2. People’s Friendship University of Russia, Moscow, Russia

    B. D. Gel’man

Authors
  1. B. D. Gel’man
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Correspondence to B. D. Gel’man.

Additional information

Russian Text © The Author (s), 2019. Published in Funktsional’ nyi Analiz i Ego Prilozheniya, 2019, Vol. 53, No. 3, pp. 84–88.

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Gel’man, B.D. Caristi’s Inequality and α-Contraction Mappings. Funct Anal Its Appl 53, 224–228 (2019). https://doi.org/10.1134/S0016266319030079

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  • DOI: https://doi.org/10.1134/S0016266319030079

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