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Link to original content: https://doi.org/10.1007/s11075-008-9260-1
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Bernstein-type operators in Chebyshev spaces

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Abstract

We prove that it is possible to construct Bernstein-type operators in any given Extended Chebyshev space and we show how they are connected with blossoms. This generalises and explains a recent result by Aldas/Kounchev/Render on exponential spaces. We also indicate why such operators automatically possess interesting shape preserving properties and why similar operators exist in still more general frameworks, e.g., in Extended Chebyshev Piecewise spaces. We address the problem of convergence of infinite sequences of such operators, and we do prove convergence for special instances of Müntz spaces.

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Authors and Affiliations

  1. Laboratoire Jean Kuntzmann, Université Joseph Fourier, BP53, 38041, Grenoble Cedex 9, France

    Marie-Laurence Mazure

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  1. Marie-Laurence Mazure
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Correspondence to Marie-Laurence Mazure.

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Mazure, ML. Bernstein-type operators in Chebyshev spaces. Numer Algor 52, 93–128 (2009). https://doi.org/10.1007/s11075-008-9260-1

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  • DOI: https://doi.org/10.1007/s11075-008-9260-1

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