Bézier–Bernstein–Durrmeyer type operators

  • Arun KajlaEmail author
  • Tuncer Acar
Original Paper


In this note, we construct the Bézier variant of the Bernstein–Durrmeyer type operators. We present local results, a direct approximation theorem by using the Ditzian–Totik modulus of smoothness and a quantitative Voronovskaja type theorem with the help of the Ditzian–Totik modulus of continuity. The rate of convergence for differential functions whose derivatives are of bounded variation is also established. Finally, we show that the numerical examples which illustrate the authenticity of the theoretical results and the effectiveness of the defined operators.


Positive approximation process Bézier operators Degree of approximation 

Mathematics Subject Classification

41A25 26A15 



The second author has been partially supported within TUBITAK (The Scientific and Technological Research Council of Turkey) 1002-Project 119F191.


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Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  1. 1.Department of MathematicsCentral University of HaryanaMahendragarhIndia
  2. 2.Department of Mathematics, Faculty of ScienceSelcuk UniversitySelcukluTurkey

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