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Approximation by modified \(U^{\rho }_n\) 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 purpose of present paper is to extend the study of \(\lambda \)-Bernstein operators introduce by Cai et al. (J Inequal Appl 12:1–11, 2018). In our paper we consider a generalization of the \(U^{\rho }_n\) operators introduced in 2007 by Radu Paltanea, using the new Bernstein–Bézier bases \(\{\tilde{b}_{n,k}\}\) with shape parameter \(\lambda \). Some approximation properties are given, including local approximation, error estimation in terms of moduli of continuity and Voronovskaja-type asymptotic formulas. Finally, we give some numerical examples and graphs to put in evidence the convergence of \(U^{\rho }_n(f;x)\) to f(x).

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Acknowledgements

The work of the first author was financed from Lucian Blaga University of Sibiu research Grants 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

  2. Department of Mathematics, Faculty of Science, Selcuk University, 42003, Konya, Turkey

    Tuncer Acar

  3. Department of Statistics-Forecasts-Mathematics, FSEGA, Babeş-Bolyai University, Cluj-Napoca, Romania

    Voichiţa Adriana Radu

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  1. Ana-Maria Acu
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  2. Tuncer Acar
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  3. Voichiţa Adriana Radu
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Correspondence to Voichiţa Adriana Radu.

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Acu, AM., Acar, T. & Radu, V.A. Approximation by modified \(U^{\rho }_n\) operators. RACSAM 113, 2715–2729 (2019). https://doi.org/10.1007/s13398-019-00655-y

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