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Convergence Properties of Genuine Bernstein–Durrmeyer Operators

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Advances in Summability and Approximation Theory

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Abstract

The genuine Bernstein–Durrmeyer operators have notable approximation properties, and many papers have been written on them. In this paper, we introduce a modified genuine Bernstein–Durrmeyer operators. Some approximation results, which include local approximation, error estimation in terms of the modulus of continuity and weighted approximation is obtained. Also, a quantitative Voronovskaya-type approximation will be studied. The convergence of these operators to certain functions is shown by illustrative graphics using MAPLE algorithms.

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Acknowledgements

The work was financed from Lucian Blaga University of Sibiu research grants LBUS-IRG-2017-03.

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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

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  1. Ana-Maria Acu
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Correspondence to Ana-Maria Acu .

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Editors and Affiliations

  1. Operator Theory and Applications Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

    S. A. Mohiuddine

  2. Department of Mathematics, Selçuk University, Selçuklu, Konya, Turkey

    Tuncer Acar

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Acu, AM. (2018). Convergence Properties of Genuine Bernstein–Durrmeyer Operators. In: Mohiuddine, S., Acar, T. (eds) Advances in Summability and Approximation Theory. Springer, Singapore. https://doi.org/10.1007/978-981-13-3077-3_5

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