Detail publikace
The discrete fractional Karamata theorem and its applications
ŘEHÁK, P.
Anglický název
The discrete fractional Karamata theorem and its applications
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
en
Originální abstrakt
We establish a fractional extension of the discrete Karamata integration theorem for two types of fractional sum operators. This result, along with other properties of regularly varying sequences and the tools such as comparison theorems and a fixed point theorem in FK-space, is then used to study asymptotic properties of solutions to a nonlinear fractional difference equation. We also establish and utilize a fractional extension of the Stolz-Ces & aacute;ro theorem, i.e., of the discrete l'Hospital rule. Both, the discrete fractional Karamata theorem and the discrete fractional l'Hospital rule, are believed to find applications in a broader context within the discrete fractional calculus.
Anglický abstrakt
We establish a fractional extension of the discrete Karamata integration theorem for two types of fractional sum operators. This result, along with other properties of regularly varying sequences and the tools such as comparison theorems and a fixed point theorem in FK-space, is then used to study asymptotic properties of solutions to a nonlinear fractional difference equation. We also establish and utilize a fractional extension of the Stolz-Ces & aacute;ro theorem, i.e., of the discrete l'Hospital rule. Both, the discrete fractional Karamata theorem and the discrete fractional l'Hospital rule, are believed to find applications in a broader context within the discrete fractional calculus.
Klíčová slova anglicky
Regularly varying sequence; Karamata integration theorem; fractional sum operator; fractional difference equation; asymptotic formula
Vydáno
28.10.2024
Nakladatel
WALTER DE GRUYTER GMBH
Místo
BERLIN
ISSN
0139-9918
Ročník
74
Číslo
5
Strany od–do
1205–1214
Počet stran
10
BIBTEX
@article{BUT190064,
author="Pavel {Řehák},
title="The discrete fractional Karamata theorem and its applications",
year="2024",
volume="74",
number="5",
month="October",
pages="1205--1214",
publisher="WALTER DE GRUYTER GMBH",
address="BERLIN",
issn="0139-9918"
}