Publication detail

The discrete fractional Karamata theorem and its applications

ŘEHÁK, P.

Original Title

The discrete fractional Karamata theorem and its applications

Type

journal article in Web of Science

Language

English

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.

Keywords

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

Authors

ŘEHÁK, P.

Released

28. 10. 2024

Publisher

WALTER DE GRUYTER GMBH

Location

BERLIN

ISBN

0139-9918

Periodical

Mathematica Slovaca

Year of study

74

Number

5

State

Slovak Republic

Pages from

1205

Pages to

1214

Pages count

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"
}