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Ekeland’s principle and the density of the Ekeland’s point in topological vector spaces. (English) Zbl 1118.49014
Summary: This research paper contains a characterization for the topology of any topological vector space ensuring that every topology such as this can be generated by a family of quasi-norms. Following this result, we present sufficient conditions for the sets of Ekeland’s points, Takhashi’s minimal elements, Caristi’s fixed points of multivalued mapping, and equilibrium points to have dense convexhull in linear topological spaces.

49J53Set-valued and variational analysis
58E30Variational principles on infinite-dimensional spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
78M50Optimization (optics)
47N10Applications of operator theory in optimization, convex analysis, programming, economics