Baskakov - Kantorovich operators reproducing affine functions
DOI:
https://doi.org/10.24193/subbmath.2021.4.11Keywords:
Baskakov-Kantorovich operators, polynomial weighted spaces, rate of convergenceAbstract
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 characterized all functions for which there is convergence in the weighted norm.References
O. Agratini, {it Kantorovich-type operators preserving affine functions}, Hacet. J. Math. Stat. 45 (6) (2016), 1657-1663.
J. Bustamante, A. Carrillo-Zentella, and J. M. Quesada, {it Direct and strong converse theorems for a general sequence of positive linear operators},
Acta Math. Hungar., 136 (1-2) (2012), 90-106.
J. Bustamante, J. M. Quesada and J. J. Merino, {it
Pointwise estimates for Baskakov operators in weighted
spaces}, to appear
Z. Ditzian and V. Totik, {it Moduli of Smoothness},
Springer, New York (1987).
Guo Feng, {it Direct and inverse approximation theorems for
Baskakov ope-rators with the Jacobi-type weight}, Abstract and Applied Analysis, (2011), Article ID 101852, 13 pages.
A. Holhoc{s}, {it Uniform weighted approximation by positive linear operators}, Stud. Univ. Babes-Bolyai
Math., 56 No. 3, (2011), 135-146.
D.S. Mitrinovi'{c}, J. Peu{c}ari'c and A. M. Fink, {it Classical and New Inequalities in
Analysis}, Kluwer Academic Publishers, Dordrecht, 1993.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.
