Variational principles in quasi-uniform spaces and quasi-gauge spaces

M. Fakhar, S. Lotfi, A. Soubeyran and J. Zafarani
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A. Soubeyran: AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique

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Abstract: In this article, we obtain an extension of the Ekeland variational principle in quasi-uniform spaces. Since the Ekeland variational principle is a type of perturbed optimization problem, the perturbations do not need to satisfy the triangle property to obtain results. We also give some equivalent results of our main results. Moreover, we present a new version of the Ekeland variational principle and its equivalent results, in the setting of quasi-gage spaces. Finally, we establish the Ekeland variational principle in a (metric) modular space as an application of our results.

Keywords: Ekeland's variational principle; quasi-uniform space; quasi-gauge space; modular space; fixed point (search for similar items in EconPapers)
Date: 2025-04-15
Note: View the original document on HAL open archive server: https://hal.science/hal-05072772v1
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Published in Optimization, 2025, pp.1-27. ⟨10.1080/02331934.2025.2490928⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05072772

DOI: 10.1080/02331934.2025.2490928

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