Detail publikace

The discrete fractional Karamata theorem and its applications

ŘEHÁK, P.

Originální název

The discrete fractional Karamata theorem and its applications

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

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.

Klíčová slova

Regularly varying sequence; Karamata integration theorem; fractional sum operator; fractional difference equation; asymptotic formula

Autoři

ŘEHÁK, P.

Vydáno

28. 10. 2024

Nakladatel

WALTER DE GRUYTER GMBH

Místo

BERLIN

ISSN

0139-9918

Periodikum

Mathematica Slovaca

Ročník

74

Číslo

5

Stát

Slovenská republika

Strany od

1205

Strany do

1214

Strany počet

10

URL

https://www.degruyter.com/document/doi/10.1515/ms-2024-0087/html

BibTex

@article{BUT190064,
  author="Pavel {Řehák}",
  title="The discrete fractional Karamata theorem and its applications",
  journal="Mathematica Slovaca",
  year="2024",
  volume="74",
  number="5",
  pages="1205--1214",
  doi="10.1515/ms-2024-0087",
  issn="0139-9918",
  url="https://www.degruyter.com/document/doi/10.1515/ms-2024-0087/html"
}