We study a Kantorovich-type modification of the operators introduced in [1] and we characterize their convergence in the -norm. We also furnish a quantitative estimate of the convergence.
@article{bwmeta1.element.bwnjournal-article-apmv63z3p273bwm,
author = {Michele Campiti and Giorgio Metafune},
title = {$L^p$-convergence of Bernstein-Kantorovich-type operators},
journal = {Annales Polonici Mathematici},
volume = {63},
year = {1996},
pages = {273-280},
zbl = {0848.41017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv63z3p273bwm}
}
Michele Campiti; Giorgio Metafune. $L^p$-convergence of Bernstein-Kantorovich-type operators. Annales Polonici Mathematici, Tome 63 (1996) pp. 273-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv63z3p273bwm/
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[001] [2] M. Campiti and G. Metafune, Evolution equations associated with recursively defined Bernstein-type operators, preprint, 1994. | Zbl 0874.41010
[002] [3] G. G. Lorentz, Bernstein Polynomials, 2nd ed., Chelsea, New York, 1986.
[003] [4] B. Sendov and V. A. Popov, The Averaged Moduli of Smoothness, Pure Appl. Math., Wiley, 1988. | Zbl 0653.65002
[004] [5] E. C. Titchmarsh, The Theory of Functions, Oxford University Press, Oxford, 1939. | Zbl 0022.14602