Asymptotic behaviour of differentiated Bernstein polynomials

Matematicki Vesnik

Volumn 61, Issue 1, 2009, Pages 53-60

  Gonska, Heiner ^a   Raşa, Ioan ^b  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b TECHNICAL UNIVERSITY OF CLUJ NAPOCA   (Romania)

Author keywords

Bernstein operators; Convex operators; k th kantorovich modification; Simultaneous approximation; Voronovskaya theorem

Indexed keywords

EID: 63649148534     PISSN: 00255165     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

1. S. N. Bernstein, Complément á l'article de E. Voronovskaya "Détermination de la forme asymptotique de l'approximation des fonctions par les polynômes de M. Bernstein", C. R. (Dokl.) Acad. Sci. URSS A (1932), 4, 86-92.
2. M. S. Floater, On the convergence of derivatives of Bernstein approximation, J. Approx. Theory, 134 (2005), 130-135.
3. H. Gonska, On the degree of approximation in Voronovskaja's theorem, Studia Univ. Babeş-Bolyai, Mathematica 52, 3 (2007), 103-116.
4. H. Gonska, P. Piţul and I. Raşa, On Peano's form of the Taylor remainder, Voronovskaja's theorem and the commutator of positive linear operators, In: "Numerical Analysis and Approximation Theory" (Proc. Int. Conf. Cluj-Napoca 2006; ed. by O. Agratini & P. Blaga), 55-80. Cluj-Napoca: Casa Carţii de Ştiinţǎ 2006.
5. D. P. Kacsó, Certain Bernstein-Durrmeyer-type Operators Preserving Linear Functions, Schriftenreihe des Fachbereichs Mathematik, Universität Duisburg-Essen, SM-DU-675 (2008).
6. k-Räume, Math. Z. 148 (1976), 23-32.
7. R. G. Mamedov, On the asymptotic value of the approximation of repeatedly differentiable functions by positive linear operators (Russian), Dokl. Akad. Nauk, 146 (1962), 1013-1016. Translated in Soviet Math. Dokl., 3 (1962), 1435-1439.
8. R. G. Mamedov, Translated in Soviet Math. Dokl., 3 (1962), 1435-1439.
9. Bl. Sendov and V. A. Popov, Convergence of the derivatives of linear positive operators (Bulgarian), Bulgar. Akad. Nauk Izv. Mat. Inst. 11 (1970), 107-115.
10. V. S. Videnskiǐ, Linear Positive Operators of Finite Rank (in Russian), Leningrad: "A.I. Gerzen" State Pedagocical Institute 1985.
11. E. V. Voronovskaya, Détermination de la forme asymptotique d'approximation par les polynômes de M. Bernstein (in Russian), C. R. (Dokl.) Acad. Sci. URSS A, 4, 79-85 (1932).