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On Bi-dimensional Second Variation

100%

Ereú J., Giménez J., Merentes N.

Commentationes Mathematicae

2012

tom 52

nr 1

In this paper we present the concept of bounded second variation of a real valued function defined on a rectangle in \(\mathbb{R}^2\). We use Hardy-Vitali type technics in the plane in order to extend the classical notion of function of bounded second variation on intervals of \(\mathbb{R}\). We introduce the class \(BV^2(I_a^b )\), of all functions of bounded second variation on a rectangle \(I_a^b \subset \mathbb{R}^2\), and show that this class can be equipped with a norm with respect to which it is a Banach space. Finally, we present two results that show that integrals of functions of first bounded variation (on \(I_a^b\)) are in \(BV^2 (I_a^b)\).

On Korenblum convex functions

100%

Lopez L. M., Ereú J., Merentes N.

Commentationes Mathematicae

2017

tom 57

nr 1

We introduce a new class of generalized convex functions called the \(\kappa\)-convex functions, based on Korenblum's concept of \(\kappa\)-decreasing functions, where \(\kappa\) is an entropy (distortion) function. We study continuity and differentiability properties of these functions, and we discuss a special subclass which is a counterpart of the class of so-called d.c. functions. We characterize this subclass in terms of the space of functions of bounded second \(\kappa\)-variation, extending a result of F. Riesz. We also present a formal structural decomposition result for the \(\kappa\)-convex functions.

Ograniczanie wyników

2 Commentationes Mathematicae

2 Ereú J.

2 Merentes N.

1 Giménez J.

1 Lopez L. M.

1 2017

1 2012

Wyniki wyszukiwania

On Bi-dimensional Second Variation

On Korenblum convex functions