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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 number of application areas of random number sequences is constantly increasing, but the desired quality of randomness may and do differ from one application domain to another. This is the reason why there is no single perfect random number generator for every application. Hence the selection of a generator has to rely on a thorough analysis of the(More)
Nowadays nuclear imaging is increasingly used for non-invasive diagnosis. The image modalities in nuclear imaging suffer of worse statistics, in comparison with computed tomography, since they are based on emission transition tomography. Thus, precise reconstruction methods that can deal with incomplete or missing measurements are needed in order to improve(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)