Functional Analysis and Its Applications

, Volume 53, Issue 3, pp 224–228 | Cite as

Caristi’s Inequality and α-Contraction Mappings

  • B. D. Gel’manEmail author


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 words

fixed 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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Copyright information

© Springer Science+Business Media, Inc. 2019

Authors and Affiliations

  1. 1.Voronezh State UniversityVoronezhRussia
  2. 2.People’s Friendship University of RussiaMoscowRussia

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