Geodesic
Ekeland variational principle for quasimetric spaces
Vestnik rossijskih universitetov. Matematika, Tome 28 (2023) no. 143, pp. 268-276

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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, functions unbounded from below.
Mots-clés : quasimetric spaces 
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     title = {Ekeland variational principle for quasimetric spaces},
     journal = {Vestnik rossijskih universitetov. Matematika},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2023_28_143_a5/}
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R. Sengupta. Ekeland variational principle for quasimetric spaces. Vestnik rossijskih universitetov. Matematika, Tome 28 (2023) no. 143, pp. 268-276. http://geodesic.mathdoc.fr/item/VTAMU_2023_28_143_a5/