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Modified Operators Interpolating at Endpoints

Author

Listed:
  • Ana Maria Acu

    (Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No. 5-7, 550012 Sibiu, Romania
    These authors contributed equally to this work.)

  • Ioan Raşa

    (Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania
    These authors contributed equally to this work.)

  • Rekha Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    These authors contributed equally to this work.)

Abstract

Some classical operators (e.g., Bernstein) preserve the affine functions and consequently interpolate at the endpoints. Other classical operators (e.g., Bernstein–Durrmeyer) have been modified in order to preserve the affine functions. We propose a simpler modification with the effect that the new operators interpolate at endpoints although they do not preserve the affine functions. We investigate the properties of these modified operators and obtain results concerning iterates and their limits, Voronovskaja-type results and estimates of several differences.

Suggested Citation

  • Ana Maria Acu & Ioan Raşa & Rekha Srivastava, 2021. "Modified Operators Interpolating at Endpoints," Mathematics, MDPI, vol. 9(17), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2051-:d:622052
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