Baskakov-Kantorovich operators reproducing affine functions: inverse results

Authors

  • Jorge Bustamante Benemerita Universidad Autonoma de Puebla, Puebla, Mexico

DOI:

https://doi.org/10.33993/jnaat511-1264

Keywords:

Baskakov-Kantorovich operatorsrators, polynomial weighted spaces, strong inverse results
Abstract views: 167

Abstract

In a previous paper the author presented a Kantorovich modification of Baskakov operators which reproduce affine functions and he provided an upper estimate for the rate of convergence in polynomial weighted spaces.

In this paper, for the same family of operators, a strong inverse inequality is given  for the case of approximation in norm.

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References

J. Bustamante, Baskakov-Kantorovich operators reproducing affine functions, Stud. Univ. Babe s-Bolyai Math., 66 (2021) no. 4, 739-756. http://dx.doi.org/10.24193/subbmath.2021.4.11 DOI: https://doi.org/10.24193/subbmath.2021.4.11

J. Bustamante, A. Carrillo-Zentella, J.M. Quesada, Direct and strong converse theorems for a general sequence of positive linear operators, Acta Math. Hungar., 136 (2012) nos. 1-2, 90-106. https://doi.org/10.1007/s10474-012-0196-5 DOI: https://doi.org/10.1007/s10474-012-0196-5

J. Bustamante, J. Merino-Garc ıa, J.M. Quesada, Baskakov operators and Jacobi weights: pointwise estimates, J. Inequal. Appl., 2021, art. no. 119, 17 pp. https://doi.org/10.1186/s13660-021-02653-4 DOI: https://doi.org/10.1186/s13660-021-02653-4

Z. Ditzian, V. Totik, Moduli of Smoothness, Springer, New York, 1987. DOI: https://doi.org/10.1007/978-1-4612-4778-4

G. Feng, Direct and inverse approximation theorems for Baskakov operators with the Jacobi-type weight, Abstr. Appl. Anal., (2011), art. id. 101852, 13 pp. https://doi.org/10.1155/2011/101852 DOI: https://doi.org/10.1155/2011/101852

Sh. Guo, Q. Qi, Strong converse inequalities for Baskakov operators, J. Approx. Theory, 124 (2003) no. 2, 219-231. https://doi.org/10.1016/S0021-9045(03)00119-9 DOI: https://doi.org/10.1016/S0021-9045(03)00119-9

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Published

2022-09-17

How to Cite

Bustamante, J. (2022). Baskakov-Kantorovich operators reproducing affine functions: inverse results. J. Numer. Anal. Approx. Theory, 51(1), 67–82. https://doi.org/10.33993/jnaat511-1264

Issue

Vol. 51 No. 1 (2022)

Section

Articles

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Copyright (c) 2022 Jorge Bustamante

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