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Kantorovich-Bernstein polynomials

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Abstract

A gap between saturation and direct-converse theorems for Kantoro-vich-Bernstein polynomials will be closed for a steady rate of convergence. The present theorems unify the above-mentioned results. Furthermore, it is shown that for steady rates our converse results are an improvement on both weak-type converse theorems and strong-weak-type converse theorems for the Kantorovich-Bernstein polynomials.

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Authors and Affiliations

  1. Department of Mathematics, University of Alberta, T6G 2G1, Edmonton, Alberta, Canada

    Zeev Ditzian

  2. Department of Mathematics, Hangzhou University, Hangzhou, China

    Xinlong Zhou

Authors
  1. Zeev Ditzian
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  2. Xinlong Zhou
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Additional information

Communicated by George G. Lorentz.AMS classification: 41A27, 41A36, 41A40.

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Ditzian, Z., Zhou, X. Kantorovich-Bernstein polynomials. Constr. Approx 6, 421–435 (1990). https://doi.org/10.1007/BF01888273

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  • DOI: https://doi.org/10.1007/BF01888273

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