Approximation by certain linking operators

Abstract

In this paper, we improve the order of approximation of certain operators linking Bernstein and genuine Bernstein–Durrmeyer operators. Firstly, we obtain some direct results in terms of modulus of continuity and Voronovskaja type asymptotic formula for these operators. Finally, we give some numerical examples regarding the obtained theoretical results for new constructed operators.

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Acknowledgements

We are grateful to the reviewers for the proposed corrections which improved our manuscript. The work was done jointly, while the first author visited Ankara University during November 2-16, 2019, supported by The Scientific and Technological Research Council of Turkey, ”2221 - Fellowships for Visiting Scientists and Scientists on Sabbatical Leave, with application number 1059B211900262”.

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Correspondence to Nursel Çetin.

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Communicated by Gradimir Milovanovic.

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Acu, A., Başcanbaz-Tunca, G. & Çetin, N. Approximation by certain linking operators. Ann. Funct. Anal. (2020). https://doi.org/10.1007/s43034-020-00081-x

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Keywords

  • Bernstein operators
  • Genuine Bernstein-Durrmeyer operators
  • Modulus of continuity
  • Voronovskaya type theorem
  • Order of approximation

Mathematics Subject Classification

  • 41A25
  • 41A36