Approximation of functions by Stancu variant of Bernstein–Kantorovich operators based on shape parameter \({\varvec{\alpha }}\)

  • S. A. MohiuddineEmail author
  • Faruk Özger
Original Paper


We construct the Stancu variant of Bernstein–Kantorovich operators based on shape parameter \(\alpha \). We investigate the rate of convergence of these operators by means of suitable modulus of continuity to any continuous functions f(x) on \(x\in [0,1]\) and Voronovskaja-type approximation theorem. Moreover, we study other approximation properties of our new operators such as weighted approximation as well as pointwise convergence. Finally, some illustrative graphics are provided here by our new Stancu-type Bernstein–Kantorovich operators in order to demonstrate the significance of our operators.


Bernstein–Kantorovich operators Rate of convergence Weighted approximation Pointwise convergence 

Mathematics Subject Classification

Primary 41A25 Secondary 41A35 41A36 



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Copyright information

© The Royal Academy of Sciences, Madrid 2020

Authors and Affiliations

  1. 1.Department of General Required Courses, Mathematics, Faculty of Applied StudiesKing Abdulaziz UniversityJeddahSaudi Arabia
  2. 2.Operator Theory and Applications Research Group, Department of MathematicsKing Abdulaziz UniversityJeddahSaudi Arabia
  3. 3.Department of Engineering Sciencesİzmir Katip Çelebi UniversityIzmirTurkey

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