Research Article

A Generalization of Szász-Baskakov Operators by using the Appell Polynomials of Class A^(2)

Volume: 37 Number: 4 December 1, 2024
EN

A Generalization of Szász-Baskakov Operators by using the Appell Polynomials of Class A^(2)

Abstract

In this paper, we obtain a generalization of the Szász-Baskakov operators with the help of A^((2)) class Appell polynomials. For every compact subset of [0,∞), the uniform convergence of these operators is provided. We also mention the convergence rate of our new operators and then we find some approximation results. The rate of convergence is obtained with the help of the Steklov function.

Keywords

References

  1. [1] Szasz, O., “Generalization of S. Bernstein’s polynomials to the infinite interval”, Jornal of Research of the National Bueau Standards, 45(3): 239–245, (1950).
  2. [2] Baskakov, V. A., “An instance of a sequence of linear positive operators in the space of continuous functions”, Doklady Akademii Nauk SSSR, 113(2): 249-251, (1957).
  3. [3] Prasad, G., Agrawal, P.N., and Kasana, H.S., “Approximation of functions on [0,∞) by a new sequence of modified Szász operators”, Mathematical Forum, 6(2): 1–11, (1983).
  4. [4] Jakimovski, A. and Leviatan, D., “Generalized Szász operators for the approximation in the infinite interval”, Mathematica (Cluj), 11(34): 97–103, (1969).
  5. [5] Ismail, MEH., “On a generalization of Szász operators”, Mathematica (Cluj), 39(2): 259–267, (1974).
  6. [6] Jeelani, M.B., and Alnahdi, A.S., “Approximation by Operators for the Sheffer–Appell Polynomials”, Symmetry, 14(12): 2672, (2022).
  7. [7] Cai, QB., Cekim, B., and Icoz, G., “Gamma generalization operators involving analytic functions”, Mathematics, 9(13): 1547, (2021).
  8. [8] Gupta, P., Acu, A.M., and Agrawal, P.N., “Jakimovski– Leviatan operators of Kantorovich type involving multiple Appell polynomials”, Georgian Mathematical Journal, 28(1): 73–82, (2021).

Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Early Pub Date

April 19, 2024

Publication Date

December 1, 2024

Submission Date

November 16, 2023

Acceptance Date

March 18, 2024

Published in Issue

Year 2024 Volume: 37 Number: 4

APA
Kanat, K., Sofyalıoğlu, M., & Karadaş, V. (2024). A Generalization of Szász-Baskakov Operators by using the Appell Polynomials of Class A^(2). Gazi University Journal of Science, 37(4), 1918-1926. https://doi.org/10.35378/gujs.1391889
AMA
1.Kanat K, Sofyalıoğlu M, Karadaş V. A Generalization of Szász-Baskakov Operators by using the Appell Polynomials of Class A^(2). Gazi University Journal of Science. 2024;37(4):1918-1926. doi:10.35378/gujs.1391889
Chicago
Kanat, Kadir, Melek Sofyalıoğlu, and Verda Karadaş. 2024. “A Generalization of Szász-Baskakov Operators by Using the Appell Polynomials of Class A^(2)”. Gazi University Journal of Science 37 (4): 1918-26. https://doi.org/10.35378/gujs.1391889.
EndNote
Kanat K, Sofyalıoğlu M, Karadaş V (December 1, 2024) A Generalization of Szász-Baskakov Operators by using the Appell Polynomials of Class A^(2). Gazi University Journal of Science 37 4 1918–1926.
IEEE
[1]K. Kanat, M. Sofyalıoğlu, and V. Karadaş, “A Generalization of Szász-Baskakov Operators by using the Appell Polynomials of Class A^(2)”, Gazi University Journal of Science, vol. 37, no. 4, pp. 1918–1926, Dec. 2024, doi: 10.35378/gujs.1391889.
ISNAD
Kanat, Kadir - Sofyalıoğlu, Melek - Karadaş, Verda. “A Generalization of Szász-Baskakov Operators by Using the Appell Polynomials of Class A^(2)”. Gazi University Journal of Science 37/4 (December 1, 2024): 1918-1926. https://doi.org/10.35378/gujs.1391889.
JAMA
1.Kanat K, Sofyalıoğlu M, Karadaş V. A Generalization of Szász-Baskakov Operators by using the Appell Polynomials of Class A^(2). Gazi University Journal of Science. 2024;37:1918–1926.
MLA
Kanat, Kadir, et al. “A Generalization of Szász-Baskakov Operators by Using the Appell Polynomials of Class A^(2)”. Gazi University Journal of Science, vol. 37, no. 4, Dec. 2024, pp. 1918-26, doi:10.35378/gujs.1391889.
Vancouver
1.Kadir Kanat, Melek Sofyalıoğlu, Verda Karadaş. A Generalization of Szász-Baskakov Operators by using the Appell Polynomials of Class A^(2). Gazi University Journal of Science. 2024 Dec. 1;37(4):1918-26. doi:10.35378/gujs.1391889

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