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- Heiner Gonska, Ioan Raşa
- 2009

The present note discusses various quantitative forms of Vor-vonovskaya's 1932 result dealing with the asymptotic behavior of the classical Bernstein operators. In particular the relationship between a result of Sikkema and van der Meer and an alternative approach of the authors ist discussed. 41A36 In a recent paper [4] the well-known theorem of… (More)

Using Taylor’s formula some inequalities for a positive linear functional are considered in this paper. These results lead us to new estimates of the differences of certain positive linear operators. Applications for some known positive linear operators are given.

We consider nonlinear algebraic systems of the form F ( x ) = Ax + p , x ∈ ℝ + n $F(x)= Ax+p, x\in \mathbb {R}^{n}_{+}$ , where A is a positive matrix and p a non-negative vector. They are involved quite naturally in many applications. For such systems we prove that a positive solution x ∗ exists and is unique. Moreover, we prove that x ∗ is an attraction… (More)

The Bernstein operators of second kind were introduced by Paolo Soardi in 1990, in terms of a random walk on a certain hypergroup. They have the same relation with Chebyshev polynomials of second kind as the classical Bernstein operators have with Chebyshev polynomials of first kind. In this paper we describe a de Casteljau type algorithm for these… (More)

We give a refined version of a non-quantitative theorem by Floater dealing with the asymptotic behaviour of differentiated Bernstein polynomials. Orderwise we thus improve a previous result by Gonska and Ra¸sa dealing with the same question. The assertion which we present here generalizes the classical Voronovskaya theorem and, in particular, a hardly known… (More)