On The Convergence Properties of Kantorovich-Szasz Type Operators Involving Tangent Polynomials

Öz

In this paper, we construct a variant of the Kantorovich Szazs type operators involving the Tangent polynomials and estimate convergence properties of these operators by using Korovkin theorem. Also we obtain the rate of convergence by using modulus of convergence and Peteer’s K-functional.

Anahtar Kelimeler

• Tangent polynomials
• Kantorovich-Szazs type operators
• Rate of convergence
• Generating functions
• Korovkin theorems

Tanjant Polinomlarını İçeren Kantorovich-Szász Tipli Operatörlerin Yakınsama Özellikleri Üzerine

Öz

Bu çalışmada, Tanjant polinomlarını içeren Kantorovich-Szász tipli operatörlerin bir varyantı oluşturulup, Korovkin teoremi kullanılarak bu operatörün yakınsaklık özellikleri tahmin edilmiştir. Ayrıca Peetre’s K- fonksiyoneli ve süreklilik modülü kullanılarak yakınsaklık hızı elde edilmiştir.

Anahtar Kelimeler

• Tangent polynomials; Kantorovich-Szász type operators; Rate of convergence; Generating functions; Korovkin theorems

Kaynakça

1. [1] Qi, F., Derivaties of tangent function and tangent numbers, Applied Mathematics and Computations, 268, 844-858, 2015.
2. [2] Ryoo, C.S., A note on the tangent numbers and polynomials, Advanced Studies in Theoretical Physics, 7(9), 447-454, 2013.
3. [3] Ryoo, C.S., On poly-tangent numbers and polynomials and the distribution of their zeros, Journal of Applied Mathematics and Informatics, 34, 487-494, 2016.
4. [4] Ryoo, C.S., Differential equations assosiated with Tangent numbers, Journal of Applied Mathematics and Informatics, 34, 487-494, 2016.
5. [5] Paltanea, R., Approximation theory using positive linear operators, Birkhauser Boston, 2004.
6. [6] Altomare, F., Campiti M. Korovkin-type approximation theory and its applications, Walter de Gruyter, 17, 2011.
7. [7] Aktaş, R., Söylemez, D., Taşdelen, F., Stancu type generalization of Szász-Durrmeyer operators involving Brenke-type polynomials, Filomat, 33(3), 855-868, 2019.
8. [8] Taşdelen, F., Aktaş, R., Altın, A., A Kantorovich type of Szász operators including Brenke-type polynomials, Abstract and Applied Analysis, 2012, 2012.

9. [9] Varma, S., Taşdelen, F., Szász type operators involving Charlier polynomials, Mathematical and Computer Modelling, 56(5-6), 118-122, 2012.
10. [10] Cekim, B., Aktaş, R., İçöz, G., Kantorovich-Stancu type operators including Boas-Buck type polynomials, Hacettepe Journal of Mathematics and Statistics, 48(2), 460-471, 2019.
11. [11] İçöz, G., Varma, S., Sucu, S., Approximation by operators including generalized Appell polynomials. Filomat, 30(2), 429-440, 2016.
12. [12] Atakut, Ç., Büyükyazıcı, İ., Approximation by Kantorovich-Szász type operators based on Brenke type polynomials, Numerical Functional Analysis and Optimization, 37(12), 1488-1502, 2016.