Ekeland's variational principle in premetric spaces

Detelina Kamburova; Nadia Zlateva

doi:10.3934/jdg.2025019

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2026, Volume 14: 64-71. Doi: 10.3934/jdg.2025019

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Ekeland's variational principle in premetric spaces

Detelina Kamburova^{1, 2, ,} and
Nadia Zlateva^1,

1.
Faculty of Mathematics and Informatics, Sofia University, 5, James Bourchier Blvd, 1164 Sofia, Bulgaria
2.
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113 Sofia, Bulgaria

^*Corresponding author: Detelina Kamburova
^*Corresponding author: Detelina Kamburova

Received: October 2024

Revised: March 2025

Early access: April 23, 2025

Published online: April 23, 2025

The study is supported by the European Union-NextGenerationEU, through the National Recovery and Resilience Plan of the Republic of Bulgaria, project BG-RRP-2.004-0008-C01.

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Abstract

We prove a variant of the Ekeland's variational principle in premetric spaces, i.e., spaces with distance function which is not symmetric and does not satisfy the triangle inequality. In the same space setting we present an extended Ekeland's variational principle and prove that it is equivalent to an Oettli-Thera type theorem. We apply the last results to get a sufficient condition for existence of a solution to the equilibrium problem.

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Mathematics Subject Classification: 49J53, 49J27, 49J45, 91B50.

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References

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