Degenerate Appell Polynomials Connecting Beta Function as a Family of Operators and Their Approximations

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Degenerate Appell Polynomials Connecting Beta Function as a Family of Operators and Their Approximations

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Degenerate Appell Polynomials Connecting Beta Function as a Family of Operators and Their Approximations

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Degenerate Appell Polynomials Connecting Beta Function as a Family of Operators and Their Approximations

ISSN

2073-8994

e-ISSN

2073-8994

Svazek periodika

—

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

14

Strana od-do

—

Kód UT WoS článku

001647315100001

EID výsledku v databázi Scopus

2-s2.0-105025967884