Charlier Polinomlarıyla İlişkili Kantorovich Tipi Operatörler Sınıfının Yaklaşım Özellikleri

Year 2023, Volume: 28 Issue: 2, 383 - 393, 31.08.2023

Kerem Gezer Mine Menekşe Yılmaz

https://doi.org/10.53433/yyufbed.1187512

Abstract

Bu çalışmada, Charlier polinom tabanlı Szász-Kantorovich tipi bir operatör tanıtıyoruz. Bu operatörlerin düzgün yakınsamasını göstermek için Korovkin teoremini kullanarak başlıyoruz. İkinci olarak, Peetre’ ın K-fonksiyonel kavramı ve operatörlerin olağan süreklilik modülü gibi matematiksel teknikleri kullanarak, operatörlerin yakınsama oranını değerlendiriyoruz Üçüncüsü, verdiğimiz operatör için asimptotik bir formül türetmek için Voronovskaya tipi yaklaşım teoremini kullanıyoruz. Son olarak Maple 2022 kullanarak sayısal bir örnek veriyoruz.

Keywords

Charlier Polinomları, düzgün yakınsaklık, Kantorovich tipi operatörler, Voronovskaja tipi teorem

Approximation Properties of a Class of Kantorovich Type Operators Associated with the Charlier Polynomials

Abstract

In this paper, we introduce a kind of Charlier polynomial-based Szász-Kantorovich type operator. We begin by using Korovkin's theorem to demonstrate the uniform convergence of these operators. Second, using mathematical techniques like Peetre’s K-functional notion and the common modulus of the operators, we evaluate the order of convergence of the operators. Third, we use the Voronovskaya type approximation theorem to derive an asymptotic formula for the operator we gave. Finally, we give a numerical example using Maple 2022.

Keywords

Charlier Polynomials, Kantorovich type operators, positive operators, Voronovskaja type theorem

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