On Functions of Bounded (φ, k)-Variation

Vector Valued Functions of Bounded Bidimensional Φ-variation

In this article we present a generalization of the concept of function of bounded variation, in the sense of Riesz, for functions defined on a rectangle in R, which take values in a Banach space. As applications, we obtain generalizations of some results due to Chistyakov and a counterpart of the classical Riesz’s Lemma.

On the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications

In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.

Functions of bounded variation on idempotent semigroups

Integral Representation of Functions of Bounded Second Φ-variation in the Sense of Schramm

In this article we introduce the concept of second Φ-variation in the sense of Schramm for normed-space valued functions defined on an interval [a, b] ⊂ R. To that end we combine the notion of second variation due to de la Vallée Poussin and the concept of φ-variation in the sense of Schramm for real valued functions. In particular, when the normed space is complete we present a characterizatio...

Functions of Bounded Higher Variation

In this paper we de ne functions of bounded n-variation, which we call BnV functions, and we establish some properties of such functions. These are a natural generalization of the space of BV functions. In particular, in the same way that the BV norm naturally allows functions with discontinuities along sets of codimension one, we show that BnV functions may have discontinuities along codimensi...