A Quantitative Variant of Voronovskaja's Theorem for King-Type Operators
A Quantitative Variant of Voronovskaja's Theorem for King-Type Operators
In this note we establish a quantitative Voronovskaja theorem for modified Bernstein polynomials using the first order Ditzian-Totik modulus of smoothness.
Keywords:
Bernstein operators, Voronovskaja theorem, King operators First order Ditzian-Totik modulus of smoothness,
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- [1] J. M. Aldaz, O. Kounchev and H. Render: Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces. Numer. Math. 114 (2009), 1–25.
- [2] Z. Ditzian and V. Totik: Moduli of Smoothness. Springer, New York, 1987.
- [3] Z. Finta: On generalized Voronovskaja theorem for Bernstein polynomials. Carpathian J. Math. 28 (2012), 231–238.
- [4] M. S. Floater: On the convergence of derivatives of Bernstein approximation. J. Approx. Theory. 134 (2005), 130–135.
- [5] H. Gonska and I. Ras ̧a: Asymptotic behavior of differentiated Bernstein polynomials. Math. Vesnik. 61 (2009), 53–60.
- [6] H. Gonska and G. Tachev: A quantitative variant of Voronovskaja’s theorem. Result. Math. 53 (2009), 287–294.
- [7] H. Gonska, M. Heilmann and I. Raşa: Asymptotic behavior of differentiated Bernstein polynomials revisited. General Math. 18 (2010), 45–53.
- [8] J. P. King: Positive linear operators which preserve x2. Acta Math. Hungar. 99 (2003), 203–208.
- ISSN: 2651-2939
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 2018
- Yayıncı: Tuncer ACAR