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In this paper, we focus on vector equilibrium problems whose final space is a real linear space not necessarily endowed with a topology. In this framework, some exact and approximate Ekeland variational principles are obtained. The main mathematical tool is a kind of strict fixed point theorem for set-valued mappings, from which the Ekeland variational principles are derived by means of algebraic notions and a concept of approximate solution for vector equilibrium problems based on free-disposal sets. The obtained results improve other recent ones of the literature, and clarify the role of some assumptions usually required on the vector bifunction to state Ekeland variational principles in vector equilibrium problems. [ABSTRACT FROM AUTHOR]

In this paper, the so-called nonconvex separation functional is studied in a real linear space not necessarily endowed with a topology. The essential properties of this functional, which are well known in the topological framework, are derived by using algebraic counterparts to the topological concepts of interior and closure. Finally, it is used to characterize, in the same algebraic setting and by scalarization, weak efficient solutions of vector equilibrium problems defined through algebraic solid ordering sets. [ABSTRACT FROM AUTHOR]