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Linearkombinationen von iterierten Bernsteinoperatoren

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Abstract

The Bernstein polynomials Bn(f) approximate every function f which is continuous on [0, 1] uniformly on [0, 1]. Also the derivatives of the Bernstein polynomials approach the derivatives of the function f uniformly on [0, 1], if f has continuous derivatives. In this paper we shall introduce polynomial operators, namely linear combinations of iterates of Bernstein operators, which have the same properties but, under definite conditions, approximate f more closely than the Bernstein operators.

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Authors and Affiliations

  1. Mathematisches Institut der Ruhr, Universität Bochum, Universitätsstr. 150, D-4630, Bochum, Bundesrepublik Deutschland

    Günter Felbecker

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  1. Günter Felbecker
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Felbecker, G. Linearkombinationen von iterierten Bernsteinoperatoren. Manuscripta Math 29, 229–248 (1979). https://doi.org/10.1007/BF01303629

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  • DOI: https://doi.org/10.1007/BF01303629

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