Refined discrete regular variation and its applications
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F19%3APU132830" target="_blank" >RIV/00216305:26210/19:PU132830 - isvavai.cz</a>
Result on the web
<a href="https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5670" target="_blank" >https://onlinelibrary.wiley.com/doi/full/10.1002/mma.5670</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mma.5670" target="_blank" >10.1002/mma.5670</a>
Alternative languages
Result language
angličtina
Original language name
Refined discrete regular variation and its applications
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA17-03224S" target="_blank" >GA17-03224S: Asymptotic theory of ordinary and fractional differential equations and their numerical discretizations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematical Methods in the Applied Sciences
ISSN
0170-4214
e-ISSN
1099-1476
Volume of the periodical
42
Issue of the periodical within the volume
18
Country of publishing house
GB - UNITED KINGDOM
Number of pages
12
Pages from-to
1-12
UT code for WoS article
000477454600001
EID of the result in the Scopus database
2-s2.0-85069701592