Degenerate Appell Polynomials Connecting Beta Function as a Family of Operators and Their Approximations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F25%3AA2603C5W" target="_blank" >RIV/61988987:17310/25:A2603C5W - isvavai.cz</a>
Result on the web
<a href="https://www.mdpi.com/2073-8994/17/12/2050" target="_blank" >https://www.mdpi.com/2073-8994/17/12/2050</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3390/sym17122050" target="_blank" >10.3390/sym17122050</a>
Alternative languages
Result language
angličtina
Original language name
Degenerate Appell Polynomials Connecting Beta Function as a Family of Operators and Their Approximations
Original language description
This paper introduces a novel family of positive linear operators constructed by blending degenerate Appell polynomials with a classical Beta kernel in the Durrmeyer setting. The operators are defined as Hn(g;u) = sum_{rho=0}^{infinity} h_rho(n+u; lambda) integral_{0}^{1} Kn(rho, t) g(t) dt, where h_rho(nu; lambda) is derived from degenerate Appell polynomials (nu denotes the product of n and u) and Kn(rho, t) is a Beta-type kernel. We establish the linearity and positivity of these operators and derive crucial moment estimates. Approximation properties are examined via Korovkin-type theorems, and the asymptotic behavior is investigated through a Voronovskaja-type theorem. The results extend and unify earlier work on Appell-based approximation operators and offer new tools for approximating functions in weighted spaces. Numerical examples and error estimates are provided to illustrate the efficacy of the proposed operators. In addition, the inherent symmetry in the structure of the proposed operators-arising from the symmetric nature of the Beta kernel and the generating functions of degenerate Appell polynomials is discussed. Such symmetry plays a key role in ensuring balanced approximation and convergence characteristics.
Czech name
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Czech description
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Classification
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
10102 - Applied mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Degenerate Appell Polynomials Connecting Beta Function as a Family of Operators and Their Approximations
ISSN
2073-8994
e-ISSN
2073-8994
Volume of the periodical
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Issue of the periodical within the volume
12
Country of publishing house
CH - SWITZERLAND
Number of pages
14
Pages from-to
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UT code for WoS article
001647315100001
EID of the result in the Scopus database
2-s2.0-105025967884