ON EKELAND VARIATIONAL PRINCIPLE FOR PREORDERED UNIFORM SPACE

Lucas Fresse†, Viorica V. Motreanu‡

Abstract: We introduce a notion of preordered uniform space which extends the classical notion of uniform space and uniformizable topological space. We establish two versions of Ekeland variational principle for the present setting. The first version is for a real-valued submonotone map in a general preordered uniform space while the second version is for a vector-valued map but within an at most countable uniform structure.

Keywords: uniform space, preordered space, submonotone map, variational principle.

MSC: 58E30, 06A75, 54E15, 49J52.

DOI 10.56082/annalsarscimath.2026.4.365

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*Accepted for publication on October 18, 2026
†lucas.fresse@univ-lorraine.fr, Université de Lorraine, Institut Élie Cartan, 54506 Vandoeuvre-lès-Nancy, France
‡vmotreanu@gmail.com, Lycée Varoquaux, 10 rue Jean Moulin, 54510 Tomblaine, France

PUBLISHED in

Annals Academy of Romanian Scientists Series on Mathematics and Its Application,

Volume 18 no 4, 2026

ISSN ONLINE 2066 – 6594
ISSN PRINT 2066 – 5997