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A new approach to improve the order of approximation of the Bernstein operators: theory and applications

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Abstract

This paper presents a new approach to improve the order of approximation of the Bernstein operators. Three new operators of the Bernstein-type with the degree of approximations one, two, and three are obtained. Also, some theoretical results concerning the rate of convergence of the new operators are proved. Finally, some applications of the obtained operators such as approximation of functions and some new quadrature rules are introduced and the theoretical results are verified numerically.

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Acknowledgment

The authors would like to thank the anonymous reviewers for their careful reading of the manuscript and their comments which improved the quality of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Mathematics Computer Sciences, Amirkabir University of Technology, No.424, Hafez Avenue, Tehran, Iran

    Hassan Khosravian-Arab & Mehdi Dehghan

  2. Department of Applied Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, P.O. Box 14115-134, Tehran, Iran

    M. R. Eslahchi

Authors
  1. Hassan Khosravian-Arab
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  2. Mehdi Dehghan
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  3. M. R. Eslahchi
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Correspondence to Mehdi Dehghan.

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Khosravian-Arab, H., Dehghan, M. & Eslahchi, M.R. A new approach to improve the order of approximation of the Bernstein operators: theory and applications. Numer Algor 77, 111–150 (2018). https://doi.org/10.1007/s11075-017-0307-z

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  • DOI: https://doi.org/10.1007/s11075-017-0307-z

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