Abstract: The present paper mainly discuss the classification of continuous and discontinuous functions of unbounded variation on closed intervals. The classification of functions of bounded variation ...

wherein the three contingencies are special cases of the more general classes of functions traditionally labelled as “slowly, regularly or rapidly varying at ”. Motivated by the fact that the ’s of ...

In this second part, we thoroughly examine the types of higher-order asymptotic variation of a function obtained by all possible basic algebraic operations on higher-order varying functions. The ...

We study the moduli of continuity of functions of bounded variation and of their variation functions. It is easy to see that the modulus of continuity of a function of bounded variation is always ...

Functions of bounded variation were introduced by C. Jordan in connexion with Dirichlet's test for the convergence of Fourier series. However, the modern definition of functions of bounded variation ...

1 Institute of Mathematics, University of Lübeck, Lübeck, Germany 2 Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine This paper ...

Functions with bounded variations are particular integrable functions whose total variations are finite. They play an important role in modern mathematical analysis. Functions with bounded variations ...

We consider a probabilistic approach to compute the Wiener–Young Φ-variation of fractal functions in the Takagi class. Here, the Φ-variation is understood as a generalization of the quadratic ...