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Approximation degree of a Kantorovich variant of Stancu operators based on Polya–Eggenberger distribution

  • P. N. Agrawal
  • Ana Maria AcuEmail author
  • Manjari Sidharth
Original Paper
  • 89 Downloads

Abstract

This paper is a continuation of the work done by Deo et al. (Appl. Math. Comput. 273, 281–289, 2016), in which the authors have established some approximation properties of the Stancu–Kantorovich operators based on Pólya–Eggenberger distribution. We obtain some direct results for these operators by means of the Lipschitz class function, the modulus of continuity and the weighted space. Also, we study an approximation theorem with the aid of the unified Ditzian–Totik modulus of smoothness \(\omega _{\phi ^{\tau }}(f;t),\,\,\,0\le \tau \le 1\) and the rate of convergence of the operators for the functions having a derivative which is locally of bounded variation on \([0,\infty )\).

Keywords

Pólya–Eggenberger distribution Lipschitz class function Ditzian–Totik modulus of smoothness Bounded variation 

Mathematics Subject Classification

41A10 41A25 41A36 

Notes

Acknowledgements

The work of the second author was financed from Lucian Blaga University of Sibiu research Grants LBUS-IRG-2017-03 and the third author is thankful to “The Ministry of Human Resource and Development”, India for the financial support to carry out the above work.

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Copyright information

© Springer-Verlag Italia S.r.l. 2017

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Department of Mathematics and InformaticsLucian Blaga University of SibiuSibiuRomania

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