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

2 years ago

(original), Approximation Theory, divided differences, Linear and positive approximation operators, not-at-ICTP, paper

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

PDF

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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

1996