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Dergiler / Turkish Journal of Mathematics and Computer Science / 2021 / Cilt: 13 - Sayı: 1

A New Generalization of Bernstein Polynomials

Harun ÇİÇEK
Aydın İZGİ
Sayfa
211–220
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
💡
Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Approximation properties · modulus of continuity · Bernstein operators

Abstract

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.

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Bu Makaleye Atıf Yap

ÇİÇEK, H., İZGİ, A. (2021). A New Generalization of Bernstein Polynomials. Turkish Journal of Mathematics and Computer Science, Cilt: 13 - Sayı: 1, 211–220. https://ajindex.com/articles/374630

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Kaynakça (17)

  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 Akad