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Zbl 1118.49014
Zhu, Jiang; Liu, Xiaolan; Postolică, Vasile
Ekeland's principle and the density of the Ekeland's point in topological vector spaces. (English)
[J] Nonlinear Anal. Forum 11, No. 2, 153-163 (2006). ISSN 1226-7228

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.

MSC 2000:: *49J53 Set-valued and variational analysis
58E30 Variational principles on infinite-dimensional spaces
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
78M50 Optimization (optics)
47N10 Appl. of operator theory in optimization, math. programming, etc.

Keywords: Ekeland's variational principle; quasi norm; Takhashi's minimal elements; Caristi's fixed points

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