Displaying similar documents to “Vectorial form of Ekeland-type variational principle in locally convex spaces and its applications.”

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.

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

J. H. Qiu, S. Rolewicz (2007)

Studia Mathematica

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The notion of local completeness is extended to locally pseudoconvex spaces. Then a general version of the Borwein-Preiss variational principle in locally complete locally pseudoconvex spaces is given, where the perturbation is an infinite sum involving differentiable real-valued functions and subadditive functionals. From this, some particular versions of the Borwein-Preiss variational principle are derived. In particular, a version with respect to the Minkowski gauge of a bounded closed...

Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

Liana Cioban, Ernö Csetnek (2013)

Open Mathematics

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Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ...