| Title:
|
Approximation by $q$-Bernstein type operators (English) |
| Author:
|
Finta, Zoltán |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
329-336 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using the $q$-Bernstein basis, we construct a new sequence $\{ L_{n} \}$ of positive linear operators in $C[0,1].$ We study its approximation properties and the rate of convergence in terms of modulus of continuity. (English) |
| Keyword:
|
$q$-integers |
| Keyword:
|
$q$-Bernstein operators |
| Keyword:
|
the Hahn-Banach theorem |
| Keyword:
|
modulus of continuity |
| MSC:
|
33D99 |
| MSC:
|
41A25 |
| MSC:
|
41A36 |
| idZBL:
|
Zbl 1249.41033 |
| idMR:
|
MR2905407 |
| DOI:
|
10.1007/s10587-011-0078-y |
| . |
| Date available:
|
2011-06-06T10:26:47Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141537 |
| . |
| Reference:
|
[1] 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. MR 0027128 |
| Reference:
|
[2] Marinescu, G.: Normed Linear Spaces.Academic Press, Bucharest (1956), Romanian. |
| Reference:
|
[3] Ostrovska, S.: The convergence of $q$-Bernstein polynomials $(0<q<1)$ in the complex plane.Math. Nachr. 282 (2009), 243-252. Zbl 1173.41004, MR 2493514, 10.1002/mana.200610735 |
| Reference:
|
[4] Phillips, G. M.: Bernstein polynomials based on the $q$-integers.Ann. Numer. Math. 4 (1997), 511-518. Zbl 0881.41008, MR 1422700 |
| Reference:
|
[5] 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. |
| Reference:
|
[6] Wang, H., Meng, F.: The rate of convergence of $q$-Bernstein polynomials for $0<q<1$.J. Approx. Theory 136 (2005), 151-158. Zbl 1082.41007, MR 2171684, 10.1016/j.jat.2005.07.001 |
| . |
