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Modified Kantorovich operators with better approximation properties

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Abstract

In the present paper, we study a new kind of Bernstein-Kantorovich-type operators. Here, we discuss a uniform convergence estimate for this modified form. Also, some direct estimates, which involve the asymptotic-type results, are established. Some numerical examples which show the relevance of the results are considered.

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Funding

The work of the third author was financed by the Lucian Blaga University of Sibiu research grant LBUS-IRG-2017-03.

Author information

Correspondence to Ana-Maria Acu.

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Gupta, V., Tachev, G. & Acu, A. Modified Kantorovich operators with better approximation properties. Numer Algor 81, 125–149 (2019). https://doi.org/10.1007/s11075-018-0538-7

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Keywords

  • Approximation by polynomials
  • Kantorovich polynomials
  • Voronovskaja-type theorem

Mathematics Subject Classification (2010)

  • 41A25
  • 41A36