Research Article
Year 2024,
Volume: 5 Issue: 2, 131 - 148, 28.11.2024
Abstract
Bu makalede, Modifiye Bernstein-Durrmeyer-Stancu tip operatörler tanımlanmıştır. Bu operatörlerin klasik olan Bernstein-Durrmeyer operatörlerden daha iyi sonuçlara sahip olduğu gösterilmiştir. Modifiye Bernstein-Durrmeyer-Stancu tip operatörler için momentleri ve merkezi momentleri hesaplanmıştır. Sonra Korovkin teoremi yardımıyla düzgün yakınsaklığı incelenmiştir. Daha sonra Voronovskaya tip teorem verilerek ele alınan operatörlerin asimptotik yaklaşımları incelenmiştir. Enson olarak elde edilen teorik sonuçlar grafik analizle incelemesi yapılmıştır.
References
- Bernstein, S. (1912). Démonstration du thèorème de Weierstrass fondée sur le calcul des probabilités. Kharkov Mathematical Society, 13(1), 1-2.
- Durrmeyer, J.L. (1967). Une formule d'inversion de la transformée de Laplace: Applications à la théorie des moments. Doctoral Dissertation, Aculté Des Sciences De I’Université De Paris, 21-28.
- Stancu, D. D. (1968). Approximation of functions by a new class of linear polynomial operators. Revue Roumaine de Mathématiques Pures et Appliquées, 13(8), 1173-1194.
- Khosravian-Arab, H., Dehghan, M., Eslahchi, M.R. (2018). A new approach to improve the order of approximation of the Bernstein operators: theory and applications. Numerical Algoritms 77(1), 111–150.
- Acu , A.M., Gupta, V., Tachev, G. (2019). Better Numerical Approximation by Durrmeyer Type Operators, Results in Mathematics, 74(90), 1-11.
- Korovkin, P.P. (1953). On convergence of linear operators in the space of continuous functions. Doklady Akademii Nauk, 90, 961-964.
- Voronovskaja, E. (1932). Determination de la forme asymptotique d’approximation des fonctions par les polynomes de M. Bernstein. Doklady Akademii Nauk SSSR 4, 79–85.
- Altomare, F., Campiti, M. (1994). Korovkin-type approximation theory and its applications. Berlin: Walter de Gruyter, 17.
- Gonska, H. (2007). On the degree of approximation in Voronovskaja’s theorem. Studia Universitatis Babeș-Bolyai Mathematica, 52(3), 103–115.
Year 2024,
Volume: 5 Issue: 2, 131 - 148, 28.11.2024
Abstract
References
- Bernstein, S. (1912). Démonstration du thèorème de Weierstrass fondée sur le calcul des probabilités. Kharkov Mathematical Society, 13(1), 1-2.
- Durrmeyer, J.L. (1967). Une formule d'inversion de la transformée de Laplace: Applications à la théorie des moments. Doctoral Dissertation, Aculté Des Sciences De I’Université De Paris, 21-28.
- Stancu, D. D. (1968). Approximation of functions by a new class of linear polynomial operators. Revue Roumaine de Mathématiques Pures et Appliquées, 13(8), 1173-1194.
- Khosravian-Arab, H., Dehghan, M., Eslahchi, M.R. (2018). A new approach to improve the order of approximation of the Bernstein operators: theory and applications. Numerical Algoritms 77(1), 111–150.
- Acu , A.M., Gupta, V., Tachev, G. (2019). Better Numerical Approximation by Durrmeyer Type Operators, Results in Mathematics, 74(90), 1-11.
- Korovkin, P.P. (1953). On convergence of linear operators in the space of continuous functions. Doklady Akademii Nauk, 90, 961-964.
- Voronovskaja, E. (1932). Determination de la forme asymptotique d’approximation des fonctions par les polynomes de M. Bernstein. Doklady Akademii Nauk SSSR 4, 79–85.
- Altomare, F., Campiti, M. (1994). Korovkin-type approximation theory and its applications. Berlin: Walter de Gruyter, 17.
- Gonska, H. (2007). On the degree of approximation in Voronovskaja’s theorem. Studia Universitatis Babeș-Bolyai Mathematica, 52(3), 103–115.
There are 9 citations in total.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Approximation Theory and Asymptotic Methods |
| Journal Section | Araştırma Makaleleri |
| Authors | |
| Publication Date | November 28, 2024 |
| Submission Date | February 23, 2024 |
| Acceptance Date | July 29, 2024 |
| Published in Issue | Year 2024 Volume: 5 Issue: 2 |