Baskakov-Kantorovich operators reproducing affine functions

Authors

  • Jorge BUSTAMANTE Benem´erita Universidad Auto´noma de Puebla, Faculty of Physic and Mathematics, Avenida San Claudio y 18 Sur, Colonia San Manuel, Ciudad Universitaria, C.P. 72570, Puebla, Mexico, e-mail: jbusta@fcfm.buap.mx https://orcid.org/0000-0003-2856-6738

DOI:

https://doi.org/10.24193/subbmath.2021.4.11

Keywords:

Baskakov-Kantorovich operators, polynomial weighted spaces, rate of convergence.

Abstract

We present a new Kantorovich modification of Baskakov operators which reproduce affine functions. We present an upper estimate for the rate of convergence of the new operators in polynomial weighted spaces and characterize all functions for which there is convergence in the weighted norm.

Mathematics Subject Classification (2010): 41A35, 41A36.

References

Agratini, O., Kantorovich-type operators preserving affine functions, Hacet. J. Math. Stat., 45(6)(2016), 1657-1663.

Bustamante, J., Carrillo-Zentella, A., Quesada, J.M., Direct and strong converse theorems for a general sequence of positive linear operators, Acta Math. Hungar., 136(2012), no. 1-2, 90-106.

Ditzian, Z., Totik, V., Moduli of Smoothness, Springer, New York, 1987.

Feng, G., Direct and inverse approximation theorems for Baskakov operators with the Jacobi-type weight, Abstr. Appl. Anal., (2011), Art. ID 101852, 13 pages.

Holhos, A., Uniform weighted approximation by positive linear operators, Stud. Univ. Babes-Bolyai Math., 56(2011), no. 3, 135-146.

Mitrinovic, D.S., Pecaric, J., Fink, A.M., Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.

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Published

2021-12-30

How to Cite

BUSTAMANTE, J. (2021). Baskakov-Kantorovich operators reproducing affine functions. Studia Universitatis Babeș-Bolyai Mathematica, 66(4), 739–756. https://doi.org/10.24193/subbmath.2021.4.11

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