On Generalized Picard Integral Operators

  • Ali AralEmail author


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.


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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