On Iterates of Linear Variation Diminishing Operators and Characterization of Bernstein-Type Polynomials

  • Ying-Sheng Hu
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique book series (ISNM, volume 90)


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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Copyright information

© Birkhäuser Verlag Basel 1989

Authors and Affiliations

  • Ying-Sheng Hu
    • 1
  1. 1.Institute of MathematicsAcademia SinicaBeijingChina

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