Charlier Polinomlarıyla İlişkili Kantorovich Tipi Operatörler Sınıfının Yaklaşım Özellikleri

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.

Anahtar Kelimeler:

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

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

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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Agrawal, P. N., & İspir, N. (2016). Degree of approximation for bivariate Chlodowsky–Szász–Charlier type operators. Results in Mathematics, 69(3-4), 369-385. doi:10.1007/s00025-015-0495-6
Ağyüz, E. (2021). On the convergence properties of Kantorovich-Szasz type operators involving tangent polynomials. Adıyaman University Journal of Science, 11(2), 244-252. doi:10.37094/adyujsci.905311
Al-Abied, A. A. H., Mursaleen, A. M., & Mursaleen, M. (2021). Szász type operators involving Charlier polynomials and approximation properties. Filomat, 35(15), 5149-5159. doi:10.2298/FIL2115149A
Ansari, K. J., Mursaleen, M., Shareef Kp, M., & Ghouse, M. (2020). Approximation by modified Kantorovich–Szász type operators involving Charlier polynomials. Advances in Difference Equations, 2020, 192. doi:10.1186/s13662-020-02645-6
Aral, A., Inoan, D., & Raşa, I. (2014). On the generalized Szász–Mirakyan operators. Results in Mathematics, 65 (3), 441-452. doi:10.1007/s00025-013-0356-0
Aslan, R. (2022). On a Stancu form Szász-Mirakjan-Kantorovich operators based on shape parameter ?. Advanced Studies: Euro-Tbilisi Mathematical Journal, 15(1), 151-166. doi:10.32513/asetmj/19322008210
Aslan, R., & Mursaleen, M. (2022). Approximation by bivariate Chlodowsky type Szász–Durrmeyer operators and associated GBS operators on weighted spaces. Journal of Inequalities and Applications, 2022(1), 1-19. doi:10.1186/s13660-022-02763-7
Atakut, Ç., & Büyükyazıcı, İ. (2010). Stancu type generalization of the Favard– Szász operators. Applied Mathematics Letters, 23(12), 1479-1482. doi:10.1016/j.aml.2010.08.017
Atakut, Ç., & Büyükyazıcı, İ. (2016). Approximation by Kantorovich-Szász type operators based on Brenke type polynomials. Numerical Functional Analysis and Optimization, 37(12), 1488-1502. doi:10.1080/01630563.2016.1216447
Ayık, A. (2018). Charlier polinomlarını içeren genelleştirilmiş Szász operatörlerinin Kantrovich tipi genelleştirilmesi. (Yüksek Lisans Tezi), Necmettin Erbakan Üniversitesi, Fen Bilimleri Enstitüsü, Konya, Türkiye.
Barbosu, D. (2004). Kantorovich-Stancu type operators. Journal of Inequalities in Pure and Applied Mathematics, 5(3), 1-6.
Çavdar, B. (2017). Szász-Charlier tipi operatörlerin gama tipi genelleştirilmesi. (Yüksek Lisans Tezi), Necmettin Erbakan Üniversitesi, Fen Bilimleri Enstitüsü, Konya, Türkiye.
Ismail, M. E. H. (2005). Classical and Quantum Orthogonal Polynomials in One Variable (Encyclopedia of Mathematics and its Applications). Cambridge, UK: Cambridge University Press. doi:10.1017/CBO9781107325982
Jakimovski, A., & Leviatan, D. (1969). Generalized Szász operators for the approximation in the infinite interval. Mathematica (Cluj), 11(34), 97-103.
Kajla, A. & Agrawal, P. N. (2016). Szász-Kantorovich type operators based on Charlier polynomials. Kyungpook Mathematical Journal, 56(3), 877-897. doi:10.5666/kmj.2016.56.3.877
Korovkin, P. P. (1953). On convergence of linear positive operators in the space of continuous functions (Russian). Doklady Akademii Nauk SSSR (NS), 90, 961–964.
Păltănea, R. (2008). Modified Szász-Mirakjan operators of integral form. Carpathian Journal of Mathematics, 24(3), 378-385.
Szasz, O. (1950). Generalization of S. Bernstein’s polynomials to the infinite interval. Journal of Research of the National Bureau of Standards, 45(3), 239-245.
Sucu, S. (2022). Stancu type operators including generalized Brenke polynomials. Filomat, 36(7), 2381-2389. doi:10.2298/FIL2207381S
Varma, S., & Taşdelen, F. (2012). Szász type operators involving Charlier polynomials. Mathematical and Computer Modelling, 56(5-6), 118-122. doi:10.1016/j.mcm.2011.12.017
Wafi, A., & Rao, N. (2016). A generalization of Szász-type operators which preserves constant and quadratic test functions. Cogent Mathematics, 3(1), 1227023. doi:10.1080/23311835.2016.1227023