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On Multivariate Bernstein Polynomials

Author

Listed:
  • Mama Foupouagnigni

    (African Institute for Mathematical Sciences, P.O. Box 608, Limbe, Cameroon
    Higher Teacher Training College, University of Yaounde I, P.O. Box 47, Yaounde, Cameroon
    These authors contributed equally to this work.)

  • Merlin Mouafo Wouodjié

    (Institute of Mathematics, University of Kassel, Heinrich-Plett Str. 40, 34132 Kassel, Germany
    These authors contributed equally to this work.)

Abstract

In this paper, we first revisit and bring together as a sort of survey, properties of Bernstein polynomials of one variable. Secondly, we extend the results from one variable to several ones, namely—uniform convergence, uniform convergence of the derivatives, order of convergence, monotonicity, fixed sign for the p -th derivative, and deduction of the upper and lower bounds of Bernstein polynomials from those of the corresponding functions.

Suggested Citation

  • Mama Foupouagnigni & Merlin Mouafo Wouodjié, 2020. "On Multivariate Bernstein Polynomials," Mathematics, MDPI, vol. 8(9), pages 1-34, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1397-:d:401942
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    References listed on IDEAS

    as
    1. Shunsheng Guo & Shujie Yue & Cuixiang Li & Ge Yang & Yiguo Sun, 1996. "A pointwise approximation theorem for linear combinations of Bernstein polynomials," Abstract and Applied Analysis, Hindawi, vol. 1, pages 1-10, January.
    2. A. Jafarian & S. Measoomy Nia & Alireza K. Golmankhaneh & D. Baleanu, 2014. "On Bernstein Polynomials Method to the System of Abel Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, May.
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