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Approximation by means of modified Bernstein operators with shifted knots

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Abstract

Usta provided a modification of Bernstein operators in 2020 that was suited for approximation on (0, 1). We define generalized Bernstein operators with shifted knots in this study. Shifted knots have the benefit of allowing approximation on the interval (0, 1) and its subintervals. It also increases the flexibility of operators for approximation. Certain theorems are derived to verify the convergence of our newly constructed operators. In addition, we provide weighted approximation theorem, Voronovskaja and Grüss Voronovskaja type theorems to demonstrate asymptotic behaviour. Graphs and tables validate the convergence of the operators for some particular cases and show the approximation error.

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Acknowledgements

The authors are grateful to the anonymous referees for their valuable suggestions leading to a better presentation of the manuscript. This work is supported by the Council of Scientific and Industrial Research (CSIR) with reference no.: 08/133(0029)/2019-EMR-I for the corresponding author.

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  1. Department of Applied Mathematics, Delhi Technological University, Bawana Road, New Delhi, Delhi, 110042, India

    Naokant Deo & Km. Lipi

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  1. Naokant Deo
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  2. Km. Lipi
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Correspondence to Km. Lipi.

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Deo, N., Lipi, K. Approximation by means of modified Bernstein operators with shifted knots. J Anal 32, 1199–1213 (2024). https://doi.org/10.1007/s41478-023-00681-5

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  • DOI: https://doi.org/10.1007/s41478-023-00681-5

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