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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)
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)