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 ...

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 ...

The anomalies in these examples make the definition of smooth variation a bit unsatisfying from a theoretical viewpoint unlike the definition of higher-order regular variation; they also show that the ...

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 ...

L. Maligranda and W. Orlicz, “On Some Properties of Functions of Generalized Variation,” Monatshefte für Mathematik, Vol. 104, No. 1, 1987, pp. 53-65. has been cited by the following article: TITLE: ...

In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval ...

Han, Xiyue , Alexander Schied, and Zhenyuan Zhang. “A limit theorem for Bernoulli convolutions and the Φ-variation of functions in the Takagi class.”.