Functions of generalized variation

Generalized Rings of Measurable and Continuous Functions

This paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

On analytic functions with generalized bounded Mocanu variation

It is well known [28] that a number of important classes of univalent functions (e.g. convex, starlike) are related through their derivatives by functions with positive real part. These functions play an important part in problem from signal theory, in moment problems and in constructing quadrature formulas, see Ronning [97] and the references cited therein for some recent applications. In this...

Generalized Α-variation and Lebesgue Equivalence to Differentiable Functions

We find an equivalent condition for a real function f : [a, b] → R to be Lebesgue equivalent to an n-times differentiable function (n ≥ 2); a simple solution in the case n = 2 appeared in an earlier paper. For that purpose, we introduce the notions of CBV G1/n and SBV G1/n functions, which play analogous rôles for the n-th order differentiability as the classical notion of a V BG∗ function for ...

On the Integral Representations of Generalized Relative Type and Generalized Relative Weak Type of Entire Functions

In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.

A Numerical Integration Method by Using Generalized Series of Functions