Publication detail
The discrete fractional Karamata theorem and its applications
ŘEHÁK, P.
English title
The discrete fractional Karamata theorem and its applications
Type
journal article in Web of Science
Language
en
Original abstract
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.
English abstract
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.
Keywords in English
Regularly varying sequence; Karamata integration theorem; fractional sum operator; fractional difference equation; asymptotic formula
Released
28.10.2024
Publisher
WALTER DE GRUYTER GMBH
Location
BERLIN
ISSN
0139-9918
Volume
74
Number
5
Pages from–to
1205–1214
Pages count
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"
}