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: 198

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.

Downloads

Download data is not yet available.

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

Downloads

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

License

Copyright (c) 2022 Jorge Bustamante

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.