Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2)

Fatih Rıza Çelik

doi:10.54287/gujsa.1912934

Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2)

Abstract

This paper studies a Durrmeyer-type family of Szász operators generated by confluent Appell polynomials of class A⁽²⁾. We investigate their approximation behavior on the semi-infinite interval in a weighted setting, obtain convergence estimates by means of the modulus of continuity and Peetre’s K-functional, and establish a Voronovskaya-type asymptotic formula. Numerical graphs are also presented for the approximation of g.

Keywords

References

Abramowitz, M., & Stegun, I. A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover Publications.
Aksoy, M. S. (2025). A generalization of Phillips operators by using the Appell polynomials of class A(2). Journal of Inequalities and Applications, 2025, 13. https://doi.org/10.1186/s13660-025-03260-3
Altomare, F., & Campiti, M. (1994). Korovkin-Type Approximation Theory and Its Applications. Walter de Gruyter. https://doi.org/10.1515/9783110884586
Appell, P. (1880). Sur une classe de polynomes. Annales Scientifiques de l'École Normale Supérieure, 9, 119-144. https://doi.org/10.24033/asens.186
Çelik, F. R., & İçöz, G. (2024). Confluent Appell polynomials of class A(2) and generalization to Szász operators. Filomat, 38(32), 11583-11592. https://doi.org/10.2298/FIL2432583C
DeVore, R. A., & Lorentz, G. G. (1993). Constructive Approximation. Springer.
Gadjiev, A. D. (1974). The convergence problem for a sequence of positive linear operators on unbounded sets and theorems analogues to that of P. P. Korovkin. Doklady Akademii Nauk SSSR, 218(5), 1001-1004.
Kanat, K., & Erdal, S. (2024). Szász–Durrmeyer operators involving confluent Appell polynomials. Axioms, 13(3), 135. https://doi.org/10.3390/axioms13030135

Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Fatih Rıza Çelik ^*
0000-0001-9482-1018
Türkiye

Publication Date

June 30, 2026

Submission Date

March 19, 2026

Acceptance Date

May 24, 2026

Published in Issue

Year 2026 Volume: 13 Number: 2

DOI

https://doi.org/10.54287/gujsa.1912934

IZ

https://izlik.org/JA73XB72AY

Cite

RIS / Bibtex

APA

Çelik, F. R. (2026). Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2). Gazi University Journal of Science Part A: Engineering and Innovation, 13(2), 746-763. https://doi.org/10.54287/gujsa.1912934

AMA

1.Çelik FR. Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2). GU J Sci, Part A. 2026;13(2):746-763. doi:10.54287/gujsa.1912934

Chicago

Çelik, Fatih Rıza. 2026. “Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2)”. Gazi University Journal of Science Part A: Engineering and Innovation 13 (2): 746-63. https://doi.org/10.54287/gujsa.1912934.

EndNote

Çelik FR (June 1, 2026) Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2). Gazi University Journal of Science Part A: Engineering and Innovation 13 2 746–763.

IEEE

[1]F. R. Çelik, “Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2)”, GU J Sci, Part A, vol. 13, no. 2, pp. 746–763, June 2026, doi: 10.54287/gujsa.1912934.

ISNAD

Çelik, Fatih Rıza. “Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2)”. Gazi University Journal of Science Part A: Engineering and Innovation 13/2 (June 1, 2026): 746-763. https://doi.org/10.54287/gujsa.1912934.

JAMA

1.Çelik FR. Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2). GU J Sci, Part A. 2026;13:746–763.

MLA

Çelik, Fatih Rıza. “Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2)”. Gazi University Journal of Science Part A: Engineering and Innovation, vol. 13, no. 2, June 2026, pp. 746-63, doi:10.54287/gujsa.1912934.

Vancouver

1.Fatih Rıza Çelik. Szász-Durrmeyer Operators Based on Confluent Appell Polynomials of Class A(2). GU J Sci, Part A. 2026 Jun. 1;13(2):746-63. doi:10.54287/gujsa.1912934