Work

Two remarks on properties of functions of bounded variation

Year: 2024

Type: article

Abstract: In terms of variations, a sufficient condition for the uniform convergence of sequences of continuous functions is proved. Using this result, we obtain an addition to the classical Helly theorem on the selection of convergent sequences of functions with uniformly bounded variations in the case when the limit function is continuous. Also, by using an example we show that the condition of continuous differentiability of a function, ensuring the differentiability of its variation with the variable upper limit, is in a certain sense sharp.

Source: Vestnik of Samara University Natural Science Series

DOI: 10.18287/2541-7525-2024-30-3-7-16

Authors: Sergey V. Astashkin, Vladislav M. Ershov

Institution: Samara National Research University

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4403836499

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