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Approximation of functions by Stancu variant of Bernstein–Kantorovich operators based on shape parameter \({\varvec{\alpha }}\)

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

Abstract

We construct the Stancu variant of Bernstein–Kantorovich operators based on shape parameter \(\alpha \). We investigate the rate of convergence of these operators by means of suitable modulus of continuity to any continuous functions f(x) on \(x\in [0,1]\) and Voronovskaja-type approximation theorem. Moreover, we study other approximation properties of our new operators such as weighted approximation as well as pointwise convergence. Finally, some illustrative graphics are provided here by our new Stancu-type Bernstein–Kantorovich operators in order to demonstrate the significance of our operators.

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Authors and Affiliations

  1. Department of General Required Courses, Mathematics, Faculty of Applied Studies, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    S. A. Mohiuddine

  2. Operator Theory and Applications Research Group, Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    S. A. Mohiuddine

  3. Department of Engineering Sciences, İzmir Katip Çelebi University, 35620, Izmir, Turkey

    Faruk Özger

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  1. S. A. Mohiuddine
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Mohiuddine, S.A., Özger, F. Approximation of functions by Stancu variant of Bernstein–Kantorovich operators based on shape parameter \({\varvec{\alpha }}\). RACSAM 114, 70 (2020). https://doi.org/10.1007/s13398-020-00802-w

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  • DOI: https://doi.org/10.1007/s13398-020-00802-w

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