Detail publikačního výsledku

Refined discrete regular variation and its applications

ŘEHÁK, P.

Originální název

Refined discrete regular variation and its applications

Anglický název

Refined discrete regular variation and its applications

Druh

Článek WoS

Originální abstrakt

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.

Anglický abstrakt

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.

Klíčová slova

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

Klíčová slova v angličtině

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

Autoři

ŘEHÁK, P.

Rok RIV

2020

Vydáno

23.07.2019

Nakladatel

John Wiley & Sons Ltd

Místo

Velká Británie

ISSN

1099-1476

Periodikum

MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Svazek

42

Číslo

18

Stát

Spojené království Velké Británie a Severního Irska

Strany od

1

Strany do

12

Strany počet

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="0170-4214",
  url="https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5670"
}