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Jain–Durrmeyer Operators Involving Inverse Pólya–Eggenberger Distribution

  • Tarul Garg
  • P. N. Agrawal
  • Arun Kajla
Research Article
  • 99 Downloads

Abstract

Stancu generalized Baskakov operators using inverse Pólya–Eggenberger distribution for a real valued bounded function on \([0,\infty )\) and a non-negative real number \(\alpha \) (which may depend on n). Dhamija and Deo (Appl Math Comput 286:15–22, 2016) introduced a Durrmeyer type modification of these generalized operators and studied the uniform convergence, the rate of convergence by means of the moduli of continuity and the Peetre’s K-functional. The purpose of the present paper is to continue to study the approximation properties of these Durrmeyer type operators. Local and global direct approximation theorems and a Voronovskaya type asymptotic theorem are established. The quantitative Voronovskaya and Grüss Voronovskaya type theorems are investigated by calculating the indispensible sixth order moment. The weighted approximation properties and the approximation of functions with derivatives of bounded variation are also studied.

Keywords

Grüss Voronovskaya type theorem Inverse Pólya–Eggenberger distribution Steklov mean Weighted approximation 

Mathematics Subject Classification

41A25 41A36 

Notes

Acknowledgements

The first author is thankful to the “Ministry of Human Resource Development, India” for financial support to carry out her research work.

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Copyright information

© The National Academy of Sciences, India 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia
  2. 2.Department of MathematicsCentral University of HaryanaHaryanaIndia

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