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Convergence Properties of Certain Positive Linear Operators

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Abstract

The present paper deals with the modified positive linear operators that present a better degree of approximation than the original ones. This new construction of operators depend on a certain function \(\varrho \) defined on [0, 1]. Some approximation properties of these operators are given. Using the first order Ditzian–Totik modulus of smoothness, some Voronovskaja type theorems in quantitative mean are proved. The main results proved in this paper are applied for Bernstein operators, Lupaş operators and genuine Bernstein–Durrmeyer operators. By numerical examples we show that depending on the choice of the function \(\varrho \), the modified operator presents a better order of approximation than the classical ones.

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Acknowledgements

Project financed from Lucian Blaga University of Sibiu research grant LBUS-IRG-2018-04.

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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 & Augusta Raţiu

  2. Science Faculty, Department of Mathematics, Gazi University, 06500, Ankara, Turkey

    Nesibe Manav

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  1. Ana-Maria Acu
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  2. Nesibe Manav
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Project financed from Lucian Blaga University of Sibiu Research Grant LBUS-IRG-2018-04.

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Acu, AM., Manav, N. & Raţiu, A. Convergence Properties of Certain Positive Linear Operators. Results Math 74, 8 (2019). https://doi.org/10.1007/s00025-018-0931-5

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