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Voronovskaya type results for special sequences of operators

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The aim of this paper is twofold. First, we present Voronovskaya type formulas that can be “differentiated” and other ones which are associated with operators preserving two prescribed functions. Then the Bernstein-Schnabl type operators \(L_n\) are considered. This sequence of positive linear operators was studied in the literature; we provide new properties of it. In particular, its Voronovskaya formula can be “differentiated” and each \(L_n\) is invariant under the Kantorovich type modification. The moments of each operator \(L_n\) form a sequence of Appell polynomials, while the central moments are constant functions.

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Acknowledgements

The authors are very grateful to the reviewers for highly valuable suggestions and remarks.

This work was supported by a Hasso Plattner Excellence Research Grant (LBUS-HPI-ERG-2020-04), financed by the Knowledge Transfer Center of the Lucian Blaga University of Sibiu.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Lucian Blaga University of Sibiu, Str. Dr. I. Ratiu, No.5-7, 550012, Sibiu, Romania

    Ana-Maria Acu & Vlad Paşca

  2. School of Mathematics and Natural Sciences, University of Wuppertal, Gaußstraße 20, 42119, Wuppertal, Germany

    Margareta Heilmann

  3. Department of Mathematics, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca, Str. Memorandumului Nr. 28, 400114, Cluj-Napoca, Romania

    Madalina Dancs & Ioan Rasa

Authors
  1. Ana-Maria Acu
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  2. Madalina Dancs
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  3. Margareta Heilmann
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  4. Vlad Paşca
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  5. Ioan Rasa
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Correspondence to Ana-Maria Acu.

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Acu, AM., Dancs, M., Heilmann, M. et al. Voronovskaya type results for special sequences of operators. RACSAM 116, 19 (2022). https://doi.org/10.1007/s13398-021-01157-6

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  • DOI: https://doi.org/10.1007/s13398-021-01157-6

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