The discrete fractional Karamata theorem and its applications

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F24%3APU152519" target="_blank" >RIV/00216305:26210/24:PU152519 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyter.com/document/doi/10.1515/ms-2024-0087/html" target="_blank" >https://www.degruyter.com/document/doi/10.1515/ms-2024-0087/html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2024-0087" target="_blank" >10.1515/ms-2024-0087</a>

Result language
angličtina
Original language name
The discrete fractional Karamata theorem and its applications
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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