| Title:
|
The sharpness of convergence results for $q$-Bernstein polynomials in the case $q>1$ (English) |
| Author:
|
Ostrovska, Sofiya |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
1195-1206 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Due to the fact that in the case $q>1$ the $q$-Bernstein polynomials are no longer positive linear operators on $C[0,1],$ the study of their convergence properties turns out to be essentially more difficult than that for $q<1.$ In this paper, new saturation theorems related to the convergence of $q$-Bernstein polynomials in the case $q>1$ are proved. (English) |
| Keyword:
|
$q$-integers |
| Keyword:
|
$q$-binomial coefficients |
| Keyword:
|
$q$-Bernstein polynomials |
| Keyword:
|
uniform convergence |
| Keyword:
|
analytic function |
| Keyword:
|
Cauchy estimates |
| MSC:
|
30E10 |
| MSC:
|
33D45 |
| MSC:
|
41A10 |
| idZBL:
|
Zbl 1174.41010 |
| idMR:
|
MR2471176 |
| . |
| Date available:
|
2010-07-21T08:15:21Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140450 |
| . |
| Reference:
|
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