On the monotonicity of a sequence of Stancu-Bernstein type operators


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.


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


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

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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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Studia Universitatis “Babes-Bolyai” Mathematica

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