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Approximation properties and error estimation of q-Bernstein shifted operators

  • Mohammad MursaleenEmail author
  • Khursheed J. Ansari
  • Asif Khan
Original Paper
  • 19 Downloads

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.

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 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Mohammad Mursaleen
    • 1
    Email author
  • Khursheed J. Ansari
    • 2
  • Asif Khan
    • 1
  1. 1.Department of MathematicsAligarh Muslim UniversityAligarhIndia
  2. 2.Department of Mathematics, College of ScienceKing Khalid UniversityAbhaSaudi Arabia

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