Posts by Octavian Agratini

Abstract


One makes a study of a sequence of Bernstein type operators, introduced and studied in [9]. These are depending on two paramters \(a\) and \(b,0\leq a\leq b\). First, one deduces a reprensntations by dividded differences for the differences of two consecutive terms of the sequence of polynomials obtained by applting these operators to a function \(f\in C\left[0,1\right]\). Using this representation, one enounces several sufficient conditions for the monotonicity of the sequence of Stancu-Bernstein polynomials.

Authors

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Bernstein polynomial; Stancu discrete operator; divided difference; convexity of first order

Paper coordinates

O. Agratini, On the monotonicity of a sequence of Stancu-Bernstein type operators, Studia Univ. ”Babeș-Bolyai”, Mathematica, 41 (1996) no. 2, pp.17-23

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About this paper

Journal

Studia Universitatis “Babes-Bolyai” Mathematica

Publisher Name

Mathematica

DOI
Print ISSN

1843-3855

Online ISSN

2065-3855

google scholar link

[1] Agratini, O., Approximation properties of class of operators of Stancu-Kantorovich type,  Preprint 1(1994), Fac. Math. Cluj-Napoca, 1-11.
[2] Della Vecchia, B.,  On the approximation of functions by means of the operators of D.D. Stancu,  Studia Univ. Babe;-Bolyai, Mathematica, XXXVII (1992), 1, 3-36.
[3] Gonska, H.H., Meier, J., Quantitative theorems approximation buy Bernstein-Stancu operators,  Calcolo, 21 (1984), 317-335.
[4] Mastroianni, G., Occorsio, M.R.,  Sulle derivate dei polinomi di Stancu,  Rend. Accad. Sci. Fis. Mat. Napoli (4), 45 (1979), 273-281.
[5] Mastroianni, G., Occorsio, M.R., Una generalizatione dell’operatore de Stancu, Ibid. (4), 45 (1979), 495-511.
[6] Mulbach, G.,  Veraligemeinerungen der Bernstein und Lagrange polynome Bemerkungen zu einer Klasse linearer Polynomoperatoren von D.D.Stancu,  Rev. Roum. Math. Pures. Appl., 15 (1970), 1235-1252.
[7] Popoviciu, T., Les functions convexes,  Acttualites Sci. Ind. No.992 (1944).
[8] Stancu, D.D., On the montonicity of the sequence formed by the first order derivatives of the Bernstein polynomials, Math. Zeitschr. 98 (1967), 46-51.
[9] Stancu, D.D., Asupra unei generalizări a polinoamelor lui B ernstein,  Studia Univ. Babeș-Bolyai, 14  (1969), fasc. 2, 31-45.

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