Publication detail

Refined discrete regular variation and its applications

ŘEHÁK, P.

Original Title

Refined discrete regular variation and its applications

Type

journal article in Web of Science

Language

English

Original Abstract

We introduce a new class of the so-called regularly varying sequences with respect to tau and state its properties. This class, on one hand, generalizes regularly varying sequences. On the other hand, it refines them and makes it possible to do a more sophisticated analysis in applications. We show a close connection with regular variation on time scales; thanks to this relation, we can use the existing theory on time scales to develop discrete regular variation with respect to tau. We reveal also a connection with generalized regularly varying functions. As an application, we study asymptotic behavior of solutions to linear difference equations; we obtain generalization and extension of known results. The theory also yields, in some way, a new view on the tests for convergence and divergence of series; we establish the statement that generalizes Raabe test and Bertrand test.

Keywords

Regularly varying sequence; Karamata theorem; time scale; difference equation; asymptotic behavior; Raabe test; Bertrand test

Authors

ŘEHÁK, P.

Released

23. 7. 2019

Publisher

John Wiley & Sons Ltd

Location

Velká Británie

ISBN

1099-1476

Periodical

Mathematical Methods in the Applied Sciences

Year of study

42

Number

18

State

United Kingdom of Great Britain and Northern Ireland

Pages from

1

Pages to

12

Pages count

12

URL

https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5670

BibTex

@article{BUT157903,
  author="Pavel {Řehák}",
  title="Refined discrete regular variation and its applications",
  journal="Mathematical Methods in the Applied Sciences",
  year="2019",
  volume="42",
  number="18",
  pages="1--12",
  doi="10.1002/mma.5670",
  issn="1099-1476",
  url="https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5670"
}