Approximation properties and error estimation of q-Bernstein shifted operators

Abstract

In the present paper, q-analogue of Lupaş Bernstein operators with shifted knots are introduced. First, some basic results for convergence of the introduced operators are established and then the rate of convergence by these operators in terms of the modulus of continuity are obtained. Further, a Voronovskaja type theorem and local approximation results for the said operators are studied. Error estimation tables are presented with respect to different parameters. We also show comparisons by some illustrative graphics for the convergence of operators to a function with the help of MATLAB R2018a.

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Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through research groups program under Grant Number R.G.P.1/13/40.

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Correspondence to Mohammad Mursaleen.

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Mursaleen, M., Ansari, K.J. & Khan, A. Approximation properties and error estimation of q-Bernstein shifted operators. Numer Algor 84, 207–227 (2020). https://doi.org/10.1007/s11075-019-00752-4

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Keywords

  • Lupaş q-Bernstein shifted operators
  • Rate of convergence
  • Modulus of continuity
  • Voronovskaja type theorem
  • K-functional
  • Local approximation

Mathematics Subject Classification (2010)

  • 41A10
  • 41A25
  • 41A36