| Title:
|
Trigonometric approximation by Nörlund type means in $L^p$-norm (English) |
| Author:
|
Szal, Bogdan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
575-589 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that the same degree of approximation as in the theorems proved by L. Leindler [Trigonometric approximation in $L^p$-norm, J. Math. Anal. Appl. 302 (2005), 129--136] and P. Chandra [Trigonometric approximation of functions in $L^p$-norm, J. Math. Anal. Appl. 275 (2002), 13--26] is valid for a more general class of lower triangular matrices. We also prove that these theorems are true under weakened assumptions. (English) |
| Keyword:
|
class $\operatorname{Lip} (\alpha,p)$ |
| Keyword:
|
$L^p$-norm |
| Keyword:
|
trigonometric approximation |
| MSC:
|
41A25 |
| MSC:
|
42A10 |
| idZBL:
|
Zbl 1212.42002 |
| idMR:
|
MR2583135 |
| . |
| Date available:
|
2009-12-22T10:04:10Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137448 |
| . |
| Reference:
|
[1] Chandra P.: Approximation by Nörlund operators.Mat. Vestnik 38 (1986), 263--269. Zbl 0655.42002, MR 0870945 |
| Reference:
|
[2] Chandra P.: Functions of classes $L^p$ and $Lip (\alpha ,p)$ and their Riesz means.Riv. Mat. Univ. Parma (4) 12 (1986), 275--282. Zbl 0853.42002, MR 0913050 |
| Reference:
|
[3] Chandra P.: A note on degree of approximation by Nörlund and Riesz operators.Mat. Vestnik 42 (1990), 9--10. Zbl 0725.42004, MR 1096908 |
| Reference:
|
[4] Chandra P.: Trigonometric approximation of functions in $L^p$-norm.J. Math. Anal. Appl. 275 (2002), 13--26. MR 1941769, 10.1016/S0022-247X(02)00211-1 |
| Reference:
|
[5] Leindler L.: Trigonometric approximation in $L^p$-norm.J. Math. Anal. Appl. 302 (2005), 129--136. MR 2107350, 10.1016/j.jmaa.2004.07.049 |
| Reference:
|
[6] Mohapatra R.N., Russell D.C.: Some direct and inverse theorem in approximation of functions.J. Austral. Math. Soc. (Ser. A) 34 (1983), 143--154. MR 0687320, 10.1017/S144678870002317X |
| Reference:
|
[7] Sahney B.N., Rao V.V.: Error bounds in the approximation of functions.Bull. Austral. Math. Soc. 6 (1972), 11--18. Zbl 0229.42009, MR 0293316, 10.1017/S0004972700044208 |
| Reference:
|
[8] Quade E.S.: Trigonometric approximation in the mean.Duke Math. J. 3 (1937), 529--542. Zbl 0017.20501, MR 1546008, 10.1215/S0012-7094-37-00342-9 |
| . |
