Learn 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)
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)
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 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)