Detail publikačního výsledku

The discrete fractional Karamata theorem and its applications

ŘEHÁK, P.

Originální název

The discrete fractional Karamata theorem and its applications

Anglický název

The discrete fractional Karamata theorem and its applications

Druh

Článek WoS

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

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

Klíčová slova v angličtině

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

Autoři

ŘEHÁK, P.

Rok RIV

2025

Vydáno

28.10.2024

Nakladatel

WALTER DE GRUYTER GMBH

Místo

BERLIN

ISSN

0139-9918

Periodikum

Mathematica Slovaca

Svazek

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"
}