Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle

J. H. Qiu; S. Rolewicz

Displaying similar documents to “Local completeness of locally pseudoconvex spaces and Borwein-Preiss variational principle”

Ekeland's variational principle in locally p-convex spaces and related results

J. H. Qiu, S. Rolewicz (2008)

Studia Mathematica

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In the framework of locally p-convex spaces, two versions of Ekeland's variational principle and two versions of Caristi's fixed point theorem are given. It is shown that the four results are mutually equivalent. Moreover, by using the local completeness theory, a p-drop theorem in locally p-convex spaces is proven.

A note on quasiconvex functions that are pseudoconvex.

Giorgio Giorgi (1987)

Trabajos de Investigación Operativa

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In the present note we consider the definitions and properties of locally pseudo- and quasiconvex functions and give a sufficient condition for a locally quasiconvex function at a point x ∈ R, to be also locally pseudoconvex at the same point.

Vectorial form of Ekeland-type variational principle in locally convex spaces and its applications.

Eshghinezhad, S., Fakhar, M. (2010)

Fixed Point Theory and Applications [electronic only]

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The strongest vector space topology is locally convex on separable linear subspaces

W. Żelazko (1997)

Annales Polonici Mathematici

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Let X be a real or complex vector space equipped with the strongest vector space topology $τ_{m a x}$ . Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.