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A Note on Approximation of Blending Type Bernstein–Schurer–Kantorovich Operators with Shape Parameter α

Author

Listed:
  • Mohammad Ayman-Mursaleen
  • Nadeem Rao
  • Mamta Rani
  • Adem Kilicman
  • Ahmed Ahmed Hussin Ali Al-Abied
  • Pradeep Malik
  • R. U. Gobithaasan

Abstract

The objective of this paper is to construct univariate and bivariate blending type α-Schurer–Kantorovich operators depending on two parameters α∈0,1 and Ï >0 to approximate a class of measurable functions on 0,1+q,q>0. We present some auxiliary results and obtain the rate of convergence of these operators. Next, we study the global and local approximation properties in terms of first- and second-order modulus of smoothness, weight functions, and by Peetre’s K-functional in different function spaces. Moreover, we present some study on numerical and graphical analysis for our operators.

Suggested Citation

  • Mohammad Ayman-Mursaleen & Nadeem Rao & Mamta Rani & Adem Kilicman & Ahmed Ahmed Hussin Ali Al-Abied & Pradeep Malik & R. U. Gobithaasan, 2023. "A Note on Approximation of Blending Type Bernstein–Schurer–Kantorovich Operators with Shape Parameter α," Journal of Mathematics, Hindawi, vol. 2023, pages 1-13, December.
    • Handle: RePEc:hin:jjmath:5245806
    DOI: 10.1155/2023/5245806
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