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On Generalized Picard Integral Operators

  • Ali AralEmail author
Chapter

Abstract

In the paper, we constructed a class of linear positive operators generalizing Picard integral operators which preserve the functions \(e^{\mu x}\) and \(e^{2\mu x},\) \(\mu >0.\) We show that these operators are approximation processes in a suitable weighted spaces. The uniform weighted approximation order of constructed operators is given via exponential weighted modulus of smoothness. We also obtain their shape preserving properties considering exponential convexity.

Keywords

Voronovskaya-type theorems Weighted modulus of continuity 

2000 Mathematics Subject Classification

Primary 41A36 Secondary 41A25 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Science and Arts, Department of MathematicsKirikkale UniversityKirikkaleTurkey

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