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Approximation properties of Lupas–Kantorovich operators based on Polya distribution

  • P. N. Agrawal
  • Nurhayat Ispir
  • Arun Kajla
Article

Abstract

In this paper, we introduce Kantorovich modification of the operators considered by Lupas and Lupas (Stud Univ Babes-Bolyai Math 32(4):61–69, 1987) based on Polya distribution and study Voronovskaja type asymptotic formula, local approximation, pointwise estimates and global approximation results. In the last section, we consider the bivariate generalization of these operators and discuss the rate of convergence. We also illustrate the convergence of these operators to some functions by graphics in Maple for both one and two dimensional cases and also estimate the error in the approximation by giving numerical examples for the bivariate case.

Keywords

Asymptotic formula Local approximation Global approximation Polya distribution 

Mathematics Subject Classification

41A25 26A15 

Notes

Acknowledgments

The authors are extremely grateful to the reviewers for a very careful reading of the manuscript and making valuable suggestions leading to a better presentation of the paper. The last author is thankful to the “University Grants Commission” India for financial support to carry out the above research work.

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Copyright information

© Springer-Verlag Italia 2015

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Department of Mathematics, Faculty of SciencesGazi UniversityAnkaraTurkey

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