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ŘEHÁK, P.
Originální název
Refined discrete regular variation and its applications
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
angličtina
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.
Klíčová slova
Regularly varying sequence; Karamata theorem; time scale; difference equation; asymptotic behavior; Raabe test; Bertrand test
Autoři
Vydáno
23. 7. 2019
Nakladatel
John Wiley & Sons Ltd
Místo
Velká Británie
ISSN
1099-1476
Periodikum
Mathematical Methods in the Applied Sciences
Ročník
42
Číslo
18
Stát
Spojené království Velké Británie a Severního Irska
Strany od
1
Strany do
12
Strany počet
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" }