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Interpolatory Pointwise Estimates for Polynomial Approximation

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Constructive Approximation Aims and scope

Abstract.

We discuss whether or not it is possible to have interpolatory pointwise estimates in the approximation of a function f∈ C[0,1] , by polynomials. For the sake of completeness, as well as in order to strengthen some existing results, we discuss briefly the situation in unconstrained approximation. Then we deal with positive and monotone constraints where we show exactly when such interpolatory estimates are achievable by proving affirmative results and by providing the necessary counterexamples in all other cases.

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Authors and Affiliations

  1. Fachbereich Mathematik gonska@informatik.uni-duisburg.de, Universität Duisburg 47048 Duisburg Germany , DE

    H. H. Gonska

  2. School of Mathematical Sciences Israel leviatan@math.tau.ac.il, Sackler Faculty of Exact Sciences Tel Aviv University Tel Aviv 69978, IL

    D. Leviatan

  3. Faculty of Mathematics and Mechanics shevchuk@imath.kiev.ua, National Taras Shevchenko University of Kyiv 252017 Kyiv Ukraine, UA

    I. A. Shevchuk

  4. Fachbereich Mathematik, wenz@informatik.uni-duisburg.de, Universität Duisburg 47048 Duisburg Germany, DE

    H. -J. Wenz

Authors
  1. H. H. Gonska
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  2. D. Leviatan
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  3. I. A. Shevchuk
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  4. H. -J. Wenz
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Additional information

November 16, 1998. Date revised: July 12, 1999. Date accepted: September 13, 1999.

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Gonska, H., Leviatan, D., Shevchuk, I. et al. Interpolatory Pointwise Estimates for Polynomial Approximation. Constr. Approx. 16, 603–629 (2000). https://doi.org/10.1007/s003650010008

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  • DOI: https://doi.org/10.1007/s003650010008

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