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Funktsional. Anal. i Prilozhen., 2019, Volume 53, Issue 3, Pages 84–88 (Mi faa3625)  

Brief communications

Karisti inequality and $\alpha$-contractive mappings

B. D. Gel'manab

a Voronezh State University
b Peoples' Friendship University of Russia, Moscow

Abstract: The article considers a new Caristi-like inequality and proves some development of the Caristi theorem on fixed points of mappings of complete metric spaces (both in the single-valued and multi-valued case). Based on the obtained theorem, we study mappings of complete metric spaces that are contractive with respect to a certain $\alpha$ function of 2 vector arguments $\alpha$-contractive mappings). This function may not be a metric or even a continuous function. Proved theorems are generalizations of the Banach principle of contraction maps of and the Nadler theorem.

Keywords: fixed point, multivalued mapping, metric space, contraction mappings.

Funding Agency Grant Number
Russian Science Foundation 17-11-01168


DOI: https://doi.org/10.4213/faa3625

Full text: PDF file (166 kB)
First page: PDF file
References: PDF file   HTML file

UDC: 517.988.6
Received: 12.10.2018
Revised: 23.05.2019
Accepted:16.05.2019

Citation: B. D. Gel'man, “Karisti inequality and $\alpha$-contractive mappings”, Funktsional. Anal. i Prilozhen., 53:3 (2019), 84–88

Citation in format AMSBIB
\Bibitem{Gel19}
\by B.~D.~Gel'man
\paper Karisti inequality and $\alpha$-contractive mappings
\jour Funktsional. Anal. i Prilozhen.
\yr 2019
\vol 53
\issue 3
\pages 84--88
\mathnet{http://mi.mathnet.ru/faa3625}
\crossref{https://doi.org/10.4213/faa3625}
\elib{https://elibrary.ru/item.asp?id=38710195}


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