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Positivity

, Volume 23, Issue 1, pp 233–246 | Cite as

Approximation properties of Szász–Mirakyan operators preserving exponential functions

  • Ali Aral
  • Daniela InoanEmail author
  • Ioan Raşa
Article
  • 65 Downloads

Abstract

This paper is a natural continuation of Acar et al. (Mediterr J Math 14:6, 2017,  https://doi.org/10.1007/s00009-016-0804-7) where Szász–Mirakyan operators preserving exponential functions are defined. As a first result, we show that the sequence of the norms of the operators, acting on weighted spaces having different weights, is uniformly bounded. Then, we prove Korovkin type approximation theorems through exponential weighted convergence. The uniform weighted approximation errors of the operators and their derivatives are characterized for exponential weights. Furthermore we give a Voronovskaya type theorem for the derivative of the operators.

Keywords

Szász–Mirakyan operators Weighted modulus of continuity Uniform convergence Voronovskaya type theorem 

Mathematics Subject Classification

41A25 41A36 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and ArtsKirikkale UniversityYahsihanTurkey
  2. 2.Department of MathematicsTechnical University of Cluj-NapocaCluj-NapocaRomania

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