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Metrically convex functions in normed spaces

Stanisław Kryński (1993)

Studia Mathematica

Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory.

Micro tangent sets of continuous functions

Zoltán Buczolich (2003)

Mathematica Bohemica

Motivated by the concept of tangent measures and by H. Fürstenberg’s definition of microsets of a compact set A we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points. The Brownian motion, on the other hand, with probability one does not have graph like, or central graph like micro tangent sets at all. Finally we show that at almost all points Takagi’s...

Minimal pairs of bounded closed convex sets

J. Grzybowski, R. Urbański (1997)

Studia Mathematica

The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.

Minkowski’s inequality and sums of squares

Péter Frenkel, Péter Horváth (2014)

Open Mathematics

Positive polynomials arising from Muirhead’s inequality, from classical power mean and elementary symmetric mean inequalities and from Minkowski’s inequality can be rewritten as sums of squares.

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