Variants of the Ekeland variational principle for approximate proper solutions of vector equilibrium problems
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DOI: 10.1007/s10898-019-00772-3
Abstract: In this paper, we provide variants of the Ekeland variational principle for a type of approximate proper solutions of a vector equilibrium problem, whose final space is finite dimensional and partially ordered by a polyhedral… read more here.
Keywords: ekeland variational; variational principle; variants ekeland; vector equilibrium ... See more keywords
Ekeland variational principles involving set perturbations in vector equilibrium problems
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DOI: 10.1007/s10898-020-00945-5
Abstract: On the basis of the notion of approximating family of cones and a generalized type of Gerstewitz’s/Tammer’s nonlinear scalarization functional, we establish variants of the Ekeland variational principle (for short, EVP) involving set perturbations for… read more here.
Keywords: ekeland variational; involving set; space; set perturbations ... See more keywords
Vectorial Ekeland variational principle for systems of equilibrium problems and its applications
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DOI: 10.1007/s11425-015-9005-4
Abstract: For a family of vector-valued bifunctions, we introduce the notion of sequentially lower monotonity, which is strictly weaker than the lower semi-continuity of the second variables of the bifunctions. Then, we give a general version… read more here.
Keywords: vectorial ekeland; sequentially lower; ekeland variational; systems equilibrium ... See more keywords
Ekeland variational principle and its equivalents in T1-quasi-uniform spaces
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DOI: 10.1080/02331934.2022.2052288
Abstract: The present paper is concerned with Ekeland Variational Principle (EkVP) and its equivalents (Caristi-Kirk fixed point theorem, Takahashi minimization principle, Oettli-Th\'era equilibrium version of EkVP) in quasi-uniform spaces. These extend some results proved by Hamel,… read more here.
Keywords: ekeland variational; gauge spaces; uniform spaces; quasi uniform ... See more keywords
A New Equilibrium Version of Ekeland's Variational Principle and Its Applications
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DOI: 10.3390/axioms11020068
Abstract: In this note, a new equilibrium version of Ekeland’s variational principle is presented. It is a modification and promotion of previous results. Subsequently, the principle is applied to discuss the equilibrium points for binary functions… read more here.
Keywords: ekeland variational; new equilibrium; equilibrium version; version ekeland ... See more keywords
Ekeland Variational Principle and Some of Its Equivalents on a Weighted Graph, Completeness and the OSC Property
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DOI: 10.3390/axioms12030247
Abstract: We prove a version of the Ekeland Variational Principle (EkVP) in a weighted graph G and its equivalence to Caristi fixed point theorem and to the Takahashi minimization principle. The usual completeness and topological notions… read more here.
Keywords: completeness; ekeland variational; osc property; principle ... See more keywords