Araştırma Makalesi
Yıl 2021,
Cilt: 13 Sayı: 1, 211 - 220, 30.06.2021
Öz
Kaynakça
- [1] Acu, A.M., Agrawal, P.N., Neer, T., Approximation properties of the modified Stancu operators, Numerical Functional Analysis and Optimization, 38(2017), 279–292.
- [2] Altomare, F., Campiti, M., Korovkin-type Approximation Theory and Its Applications, Walter de Gruyter, 1962.
- [3] Aslan, R., İzgi, A., Some approximation results on modified q-Bernstein operators, Journal of Mathematical Analysis, 11(1)(2020), 58–70.
- [4] Bernstein, S.N., Demonstration du theoreme de Weierstrass fondee sur la calcul des probabilities, Comm. Soc. Math., 2(1912), 1–2.
- [5] Chen, X., Tan, J., Liu, Z.,Xie, J., Approximation of functions by a new family of generalized Bernstein operators, Journal of Mathematical Analysis and Applications, 450(2017), 244–261.
- [6] Deo, N.,Noor M.A.,Siddiqui M.A., On approximation by a class of new Bernstein type operators, Applied mathematics and computation, 201(2008), 604–612.
- [7] Izgı, A., Approximation by a class of new type Bernstein polynomials of one and two variables, Global Journal of Pure and Applied Mathematics, 8(2012), 55–71.
- [8] Jafari, H.,Tajadodi, H., Ganji, R.M., A numerical approach for solving variable order di erential equations based on Bernstein polynomials, Computational and Mathematical Methods, 5(2019), e1055.
- [9] Jiang, B., Yu, D., On approximation by Stancu type Bernstein–Schurer polynomials in compact disks, Results in Mathematics, 72(2017), 1623–1638.
- [10] Karahan, D., İzgi, A., On approximation properties of (p, q)-Bernstein operators, European Journal of Pure and Applied Mathematics, 11(2018), 457–467.
- [11] Korovkin, P.P., On convergence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk SSSR, 90(1953), 961–964.
- [12] Lorentz, G.G., Bernstein Polynomials, American Mathematical Soc., New York, 2013.
- [13] Mursaleen, M., Ansari, K., Khan,A., On (p, q)-analogue of Bernstein operators, Applied Mathematics and Computation, 266(2015), 874–882.
- [14] Phillips, G.M., Bernstein polynomials based on the q-integers, Annals of Numerical Mathematics, 4(1997), 511–518.
- [15] Schurer, F., Linear Positive Operators in Approximation Theory, Math. Inst., Techn. Univ. Delf Report, Delft, 1962.
- [16] Stancu, D.D., Approximation of functions by a new class of linear polynomial operators, Rev. Roumaine Math. Pures Appl, 13(1968), 1173– 1194.
- [17] Weierstrass, K., Über die analytische Darstellbarkeit sogenannter willku¨rlicher Functionen einer reellen Veranderlichen, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin, 2(1885), 633–639.
Yıl 2021,
Cilt: 13 Sayı: 1, 211 - 220, 30.06.2021
Öz
We will hereby introduce a new generalization of the Schurer, Stancu, Deo, and Izgi operators which are the modifications of the Bernstein polynomials and calculate the rate of approximation for the new operator with the help of the continuity module. Then, by using graphs and numerical values, we will demonstrate that the new general operator yields better results than the above classical operators which can be seen as the basis of the approximation theory.
Anahtar Kelimeler
Approximation properties modulus of continuity Bernstein operators
Kaynakça
- [1] Acu, A.M., Agrawal, P.N., Neer, T., Approximation properties of the modified Stancu operators, Numerical Functional Analysis and Optimization, 38(2017), 279–292.
- [2] Altomare, F., Campiti, M., Korovkin-type Approximation Theory and Its Applications, Walter de Gruyter, 1962.
- [3] Aslan, R., İzgi, A., Some approximation results on modified q-Bernstein operators, Journal of Mathematical Analysis, 11(1)(2020), 58–70.
- [4] Bernstein, S.N., Demonstration du theoreme de Weierstrass fondee sur la calcul des probabilities, Comm. Soc. Math., 2(1912), 1–2.
- [5] Chen, X., Tan, J., Liu, Z.,Xie, J., Approximation of functions by a new family of generalized Bernstein operators, Journal of Mathematical Analysis and Applications, 450(2017), 244–261.
- [6] Deo, N.,Noor M.A.,Siddiqui M.A., On approximation by a class of new Bernstein type operators, Applied mathematics and computation, 201(2008), 604–612.
- [7] Izgı, A., Approximation by a class of new type Bernstein polynomials of one and two variables, Global Journal of Pure and Applied Mathematics, 8(2012), 55–71.
- [8] Jafari, H.,Tajadodi, H., Ganji, R.M., A numerical approach for solving variable order di erential equations based on Bernstein polynomials, Computational and Mathematical Methods, 5(2019), e1055.
- [9] Jiang, B., Yu, D., On approximation by Stancu type Bernstein–Schurer polynomials in compact disks, Results in Mathematics, 72(2017), 1623–1638.
- [10] Karahan, D., İzgi, A., On approximation properties of (p, q)-Bernstein operators, European Journal of Pure and Applied Mathematics, 11(2018), 457–467.
- [11] Korovkin, P.P., On convergence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk SSSR, 90(1953), 961–964.
- [12] Lorentz, G.G., Bernstein Polynomials, American Mathematical Soc., New York, 2013.
- [13] Mursaleen, M., Ansari, K., Khan,A., On (p, q)-analogue of Bernstein operators, Applied Mathematics and Computation, 266(2015), 874–882.
- [14] Phillips, G.M., Bernstein polynomials based on the q-integers, Annals of Numerical Mathematics, 4(1997), 511–518.
- [15] Schurer, F., Linear Positive Operators in Approximation Theory, Math. Inst., Techn. Univ. Delf Report, Delft, 1962.
- [16] Stancu, D.D., Approximation of functions by a new class of linear polynomial operators, Rev. Roumaine Math. Pures Appl, 13(1968), 1173– 1194.
- [17] Weierstrass, K., Über die analytische Darstellbarkeit sogenannter willku¨rlicher Functionen einer reellen Veranderlichen, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin, 2(1885), 633–639.
Toplam 17 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 13 Sayı: 1 |