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Some New Results on Bicomplex Bernstein Polynomials

Author

Listed:
  • Carlo Cattani

    (Engineering School, DEIM, Tuscia University, 01100 Viterbo, Italy)

  • Çíğdem Atakut

    (Department of Mathematics, Ankara University, Ankara 06100, Turkey)

  • Özge Özalp Güller

    (Department of Mathematics, Ankara University, Ankara 06100, Turkey)

  • Seda Karateke

    (Department of Computer Engineering, Istanbul Ayvansaray University, Istanbul 34087, Turkey)

Abstract

The aim of this work is to consider bicomplex Bernstein polynomials attached to analytic functions on a compact C 2 -disk and to present some approximation properties extending known approximation results for the complex Bernstein polynomials. Furthermore, we obtain and present quantitative estimate inequalities and the Voronovskaja-type result for analytic functions by bicomplex Bernstein polynomials.

Suggested Citation

  • Carlo Cattani & Çíğdem Atakut & Özge Özalp Güller & Seda Karateke, 2021. "Some New Results on Bicomplex Bernstein Polynomials," Mathematics, MDPI, vol. 9(21), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2748-:d:667906
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    References listed on IDEAS

    as
    1. Alexandra Ciupa, 2006. "A Voronovskaya-type theorem for a positive linear operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-7, February.
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