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On the Constants in Videnskiĭ Type Inequalities for Bernstein Operators

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Abstract

This paper deals with the approximation of functions by Bernstein operators. Specifically, the interest is mainly focused on the constants in Videnskiĭ type inequalities, which turn out to be quantitative versions of the well known Voronovskaja formula. The central moments of the even orders 6 and 8 play a key role. New upper bounds for them are proved.

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Acknowledgements

The author thanks deeply the anonymous referee for her/his remarks and suggestions that encouraged him to write a version of the paper better than the one originally submitted.

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  1. Departamento de Matemáticas, Universidad de Jaén, 23071, Jaén, Spain

    Daniel Cárdenas-Morales

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  1. Daniel Cárdenas-Morales
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Correspondence to Daniel Cárdenas-Morales.

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The author is partially supported by Research Projects DGA (E-64), MTM2015-67006-P, by FEDER funds, and by Junta de Andalucía Research Group FQM-0178.

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Cárdenas-Morales, D. On the Constants in Videnskiĭ Type Inequalities for Bernstein Operators. Results Math 72, 1437–1448 (2017). https://doi.org/10.1007/s00025-017-0707-3

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  • DOI: https://doi.org/10.1007/s00025-017-0707-3

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