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Approximation Properties of King Type \((p,\,q)\)-Bernstein Operators

  • Özge Dalmanoğlu
  • Mediha ÖrkcüEmail author
Research Paper
  • 66 Downloads

Abstract

The present paper deals mainly with a King type modification of \(( p,\,q) \)-Bernstein operators. By improving the conditions given in Mursaleen et al. (On (p, q)-analogue of Bernstein operators. Appl Math Comput 266:874–882, 2015a), we investigate the Korovkin type approximation of both \(( p,\,q) \)-Bernstein and King type \(( p,\,q) \)-Bernstein operators. We also prove that the error estimation of King type of the operator is better than that of the classical one whenever \(0\le x\le \frac{1}{3}.\)

Keywords

\((p,\,q)\)-integers \((p,\,q)\)-Bernstein Operators King type operators Rate of convergence 

Notes

Acknowledgements

We would like to thank the referees for their suggestions that improved the presentation of the paper.

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Copyright information

© Shiraz University 2017

Authors and Affiliations

  1. 1.Department of Mathematics EducationBaskent UniversityAnkaraTurkey
  2. 2.Department of Mathematics, Faculty of SciencesGazi UniversityAnkaraTurkey

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