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Approximation properties of Bernstein–Durrmeyer type operators

Author

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  • Cárdenas-Morales, D.
  • Garrancho, P.
  • Raşa, I.

Abstract

This paper deals with the approximation of continuous functions by sequences of some modified Bernstein–Durrmeyer type operators that reproduce certain test functions. The orders of approximation of the new versions turn to be at least as good as the one of the genuine Bernstein–Durrmeyer operators. Moreover, by extrapolating techniques recently applied to the classical Bernstein operators, we present a one-parameter family of modified sequences of operators that reproduce certain polynomials and possess that popular genuine sequence as a limit case. Comparisons and some illustrative graphics are also presented.

Suggested Citation

  • Cárdenas-Morales, D. & Garrancho, P. & Raşa, I., 2014. "Approximation properties of Bernstein–Durrmeyer type operators," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1-8.
    • Handle: RePEc:eee:apmaco:v:232:y:2014:i:c:p:1-8
    DOI: 10.1016/j.amc.2014.01.046
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    References listed on IDEAS

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    1. Vijay Gupta & Nurhayat Ispir, 2004. "On simultaneous approximation for some modified Bernstein-type operators," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-8, January.
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    Cited by:

    1. Birou, Marius Mihai, 2015. "A class of Markov type operators which preserve ej,j⩾1," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 1-11.

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