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Convergence Properties of Certain Positive Linear Operators

  • Ana-Maria Acu
  • Nesibe ManavEmail author
  • Augusta Raţiu
Article
  • 72 Downloads

Abstract

The present paper deals with the modified positive linear operators that present a better degree of approximation than the original ones. This new construction of operators depend on a certain function \(\varrho \) defined on [0, 1]. Some approximation properties of these operators are given. Using the first order Ditzian–Totik modulus of smoothness, some Voronovskaja type theorems in quantitative mean are proved. The main results proved in this paper are applied for Bernstein operators, Lupaş operators and genuine Bernstein–Durrmeyer operators. By numerical examples we show that depending on the choice of the function \(\varrho \), the modified operator presents a better order of approximation than the classical ones.

Keywords

Voronovskaja type theorem Ditzian–Totik modulus of smoothness linear positive operators 

Mathematics Subject Classification

Primary 41A10 Secondary 41A25 41A36 

Notes

Acknowledgements

Project financed from Lucian Blaga University of Sibiu research grant LBUS-IRG-2018-04.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics and InformaticsLucian Blaga University of SibiuSibiuRomania
  2. 2.Science Faculty, Department of MathematicsGazi UniversityAnkaraTurkey

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