Research Article
Year 2025,
Early View, 1 - 1
Abstract
References
- [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] 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] 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] Jakimovski, A. and Leviatan, D., “Generalized Szász operators for the approximation in the infinite interval”, Mathematica (Cluj), 11(34): 97–103, (1969).
- [5] Ismail, MEH., “On a generalization of Szász operators”, Mathematica (Cluj), 39(2): 259–267, (1974).
- [6] Jeelani, M.B., and Alnahdi, A.S., “Approximation by Operators for the Sheffer–Appell Polynomials”, Symmetry, 14(12): 2672, (2022).
- [7] Cai, QB., Cekim, B., and Icoz, G., “Gamma generalization operators involving analytic functions”, Mathematics, 9(13): 1547, (2021).
- [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).
- [9] Srivastava, H.M., Icoz, G., and Cekim, B., “Approximation properties of an extended family of the Szász–Mirakjan Beta-type operators”, Axioms, 8(4): 111, (2019).
- [10] Kazmin, Y.A., “On Appell polynomials”, Matematicheskie Zametki, (6): 161-172, (1969). English translation in Math Notes, (5): 556-562, (1969).
- [11] Varma, S. and Sucu, S., “A generalization of Szász operators by using the Appell polynomials of class A (2)”, Symmetry, 14(7): 1410, (2022).
- [12] Sofyalıoglu, M. and Kanat, K., “Approximation by Szász-Baskakov operators based on Boas-Buck-type polynomials”, Filomat, 36(11): 3655–3673, (2022).
- [13] Altomare, F., and Campiti, M., “Korovkin-type approximation theory and its applications”, Korovkin-type Approximation Theory and Its Applications, De Gruyter, (2011).
- [14] Gavrea, I. and Rasa, I., “Remarks on some quantitative Korovkin-type results”, Revue d’analyse numérique et de théorie de l’approximation, 22(2): 173–176, (1993).
- [15] Zhuk, V., “Functions of the Lip 1 class and SN Bernstein’s polynomials”, Vestnik Leningradskogo Universiteta Matematika Mekhanika Astronomiya, 1: 25– 30, (1989).
- [16] Fink, A.M., “Kolmogorov-Landau inequalities for monotone functions”, Journal of Mathematical Analysis and Application, 90(1): 251–258, (1982).
Year 2025,
Early View, 1 - 1
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
Szász -Baskakov operators A^((2)) class Appell polynomials Modulus of continuity Steklov function.
References
- [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] 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] 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] Jakimovski, A. and Leviatan, D., “Generalized Szász operators for the approximation in the infinite interval”, Mathematica (Cluj), 11(34): 97–103, (1969).
- [5] Ismail, MEH., “On a generalization of Szász operators”, Mathematica (Cluj), 39(2): 259–267, (1974).
- [6] Jeelani, M.B., and Alnahdi, A.S., “Approximation by Operators for the Sheffer–Appell Polynomials”, Symmetry, 14(12): 2672, (2022).
- [7] Cai, QB., Cekim, B., and Icoz, G., “Gamma generalization operators involving analytic functions”, Mathematics, 9(13): 1547, (2021).
- [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).
- [9] Srivastava, H.M., Icoz, G., and Cekim, B., “Approximation properties of an extended family of the Szász–Mirakjan Beta-type operators”, Axioms, 8(4): 111, (2019).
- [10] Kazmin, Y.A., “On Appell polynomials”, Matematicheskie Zametki, (6): 161-172, (1969). English translation in Math Notes, (5): 556-562, (1969).
- [11] Varma, S. and Sucu, S., “A generalization of Szász operators by using the Appell polynomials of class A (2)”, Symmetry, 14(7): 1410, (2022).
- [12] Sofyalıoglu, M. and Kanat, K., “Approximation by Szász-Baskakov operators based on Boas-Buck-type polynomials”, Filomat, 36(11): 3655–3673, (2022).
- [13] Altomare, F., and Campiti, M., “Korovkin-type approximation theory and its applications”, Korovkin-type Approximation Theory and Its Applications, De Gruyter, (2011).
- [14] Gavrea, I. and Rasa, I., “Remarks on some quantitative Korovkin-type results”, Revue d’analyse numérique et de théorie de l’approximation, 22(2): 173–176, (1993).
- [15] Zhuk, V., “Functions of the Lip 1 class and SN Bernstein’s polynomials”, Vestnik Leningradskogo Universiteta Matematika Mekhanika Astronomiya, 1: 25– 30, (1989).
- [16] Fink, A.M., “Kolmogorov-Landau inequalities for monotone functions”, Journal of Mathematical Analysis and Application, 90(1): 251–258, (1982).
There are 16 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Approximation Theory and Asymptotic Methods |
| Journal Section | Research Article |
| Authors | |
| Early Pub Date | April 19, 2024 |
| Publication Date | |
| Submission Date | November 16, 2023 |
| Acceptance Date | March 18, 2024 |
| Published in Issue | Year 2025 Early View |