ESTONIAN ACADEMY
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akadeemia kirjastus
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of the estonian academy of sciences
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A Voronovskaya-type theorem for the second derivative of the Bernstein–Chlodovsky polynomials; pp. 9–19
PDF | doi: 10.3176/proc.2012.1.02

Author
Harun Karsli
Abstract

This paper is devoted to a Voronovskaya-type theorem for the second derivative of the Bernstein–Chlodovsky polynomials. This type of theorem was considered for the Bernstein–Chlodovsky polynomials by Jerzy Albrycht and Jerzy Radecki in 1960 and by Paul L. Butzer and the author in 2009, in case of the polynomials themselves and their first derivative, respectively.

References

1. Albrycht, J. and Radecki, J. On a generalization of the theorem of Voronovskaya. Zeszyty Naukowe UAM Poznań, 1960, 2, 1–7.

2. Bardaro, C., Butzer, P. L., Stens, R. L., and Vinti, G. Convergence in variation and rates of approximation for Bernstein-type polynomials and singular convolution integrals. Analysis (Munich), 2003, 23(4), 299–346.

3. Butzer, P. L. and Karsli, H. Voronovskaya-type theorems for derivatives of the Bernstein–Chlodovsky polynomials and the Szász–Mirakyan operator. Comment. Math., 2009, 49(1), 33–57.

4. Chlodovsky, I. Sur le développement des fonctions définies dans un intervalle infini en séries de polynomes de M. S. Bernstein. Compositio Math., 1937, 4, 380–393.

5. Lorentz, G. G. Bernstein Polynomials. University of Toronto Press, Toronto, 1953.

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