Abstract
As we all know, Bernstein approximation of a smooth function on [a,b] preserves the signs of function itself and its higher order derivatives. This beautiful property, in one hand, wins important and wide applications,but on the other hand,has to pay a precious price--very slow convergence.It is interesting to notice that the similar situation appear,more or less,in some other wellknown approximations,for instance, the Modified Bernstein-Durrmeyer operator and Schoenberg variation diminishing operator (see[1]).
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© 1989 Birkhäuser Verlag Basel
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Hu, YS. (1989). On Iterates of Linear Variation Diminishing Operators and Characterization of Bernstein-Type Polynomials. In: Multivariate Approximation Theory IV. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 90. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7298-0_20
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DOI: https://doi.org/10.1007/978-3-0348-7298-0_20
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