Approximation by -Bernstein type operators
Czechoslovak Mathematical Journal (2011)
- Volume: 61, Issue: 2, page 329-336
- ISSN: 0011-4642
Access Full Article
top
Abstract
topHow to cite
topFinta, Zoltán. "Approximation by $q$-Bernstein type operators." Czechoslovak Mathematical Journal 61.2 (2011): 329-336. <http://eudml.org/doc/196803>.
@article{Finta2011,
abstract = {Using the $q$-Bernstein basis, we construct a new sequence $\lbrace L_\{n\} \rbrace $ of positive linear operators in $C[0,1].$ We study its approximation properties and the rate of convergence in terms of modulus of continuity.},
author = {Finta, Zoltán},
journal = {Czechoslovak Mathematical Journal},
keywords = {$q$-integers; $q$-Bernstein operators; the Hahn-Banach theorem; modulus of continuity; -integer; -Bernstein operator; the Hahn-Banach theorem; modulus of continuity},
language = {eng},
number = {2},
pages = {329-336},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Approximation by $q$-Bernstein type operators},
url = {http://eudml.org/doc/196803},
volume = {61},
year = {2011},
}
TY - JOUR
AU - Finta, Zoltán
TI - Approximation by $q$-Bernstein type operators
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 329
EP - 336
AB - Using the $q$-Bernstein basis, we construct a new sequence $\lbrace L_{n} \rbrace $ of positive linear operators in $C[0,1].$ We study its approximation properties and the rate of convergence in terms of modulus of continuity.
LA - eng
KW - $q$-integers; $q$-Bernstein operators; the Hahn-Banach theorem; modulus of continuity; -integer; -Bernstein operator; the Hahn-Banach theorem; modulus of continuity
UR - http://eudml.org/doc/196803
ER -
References
top- Kreĭn, M. G., Rutman, M. A., Linear operators leaving invariant a cone in a Banach space, Usp. Mat. Nauk (N.S.) 3 (1948), 3-95 Russian English translation: Amer. Math. Soc. Translation 1950 (1950), 128 pp. (1950) MR0027128
- Marinescu, G., Normed Linear Spaces, Academic Press, Bucharest (1956), Romanian. (1956)
- Ostrovska, S., 10.1002/mana.200610735, Math. Nachr. 282 (2009), 243-252. (2009) Zbl1173.41004MR2493514DOI10.1002/mana.200610735
- Phillips, G. M., Bernstein polynomials based on the -integers, Ann. Numer. Math. 4 (1997), 511-518. (1997) Zbl0881.41008MR1422700
- Videnskii, V. S., On the polynomials with respect to the generalized Bernstein basis, In: Problems of modern mathematics and mathematical education, Hertzen readings. St-Petersburg (2005), 130-134 Russian. (2005)
- Wang, H., Meng, F., 10.1016/j.jat.2005.07.001, J. Approx. Theory 136 (2005), 151-158. (2005) Zbl1082.41007MR2171684DOI10.1016/j.jat.2005.07.001
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.