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Russian Universities Reports. Mathematics, 2023, Volume 28, Issue 143, Pages 268–276
DOI: https://doi.org/10.20310/2686-9667-2023-28-143-268-276
(Mi vtamu296)
 

Scientific articles

Ekeland variational principle for quasimetric spaces

R. Senguptaab

a Skolkovo Institute of Science and Technology
b Derzhavin Tambov State University
References:
Abstract: In this paper, we study real-valued functions defined on quasimetric spaces. A generalization of Ekeland's variational principle and a similar statement from the article [S. Cobzas, “Completeness in quasi-metric spaces and Ekeland Variational Principle”, Topology and its Applications, vol. 158, no. 8, pp. 1073–1084, 2011] is obtained for them. The modification of the variational principle given here is applicable, in particular, to a wide class of functions unbounded from below. The result obtained is applied to the study the minima of functions defined on quasimetric spaces. A Caristi-type condition is formulated for conjugate-complete quasimetric spaces. It is shown that the proposed Caristi-type condition is a sufficient condition for the existence of a minimum for lower semicontinuous functions acting in conjugate-complete quasimetric spaces.
Keywords: Ekeland variational principle, quasimetric spaces, functions unbounded from below.
Funding agency Grant number
Russian Science Foundation 23-11-20020
The research was supported by the Russian Science Foundation (project no. 23-11-20020, https://rscf.ru/en/project/23-11-20020/).
Received: 15.07.2023
Accepted: 12.09.2023
Document Type: Article
UDC: 517, 515.124.2
MSC: 58E30, 54A05
Language: Russian
Citation: R. Sengupta, “Ekeland variational principle for quasimetric spaces”, Russian Universities Reports. Mathematics, 28:143 (2023), 268–276
Citation in format AMSBIB
\Bibitem{Sen23}
\by R.~Sengupta
\paper Ekeland variational principle for quasimetric spaces
\jour Russian Universities Reports. Mathematics
\yr 2023
\vol 28
\issue 143
\pages 268--276
\mathnet{http://mi.mathnet.ru/vtamu296}
\crossref{https://doi.org/10.20310/2686-9667-2023-28-143-268-276}
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