| Title:
|
On $|A, \delta |_{k}$-summability of orthogonal series (English) |
| Author:
|
Krasniqi, Xhevat Z. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
137 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
17-25 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the paper, we prove two theorems on $|A, \delta |_{k}$ summability, $1\leq k\leq 2$, of orthogonal series. Several known and new results are also deduced as corollaries of the main results. (English) |
| Keyword:
|
orthogonal series |
| Keyword:
|
matrix summability |
| MSC:
|
40A05 |
| MSC:
|
40C05 |
| MSC:
|
40D15 |
| MSC:
|
40F05 |
| MSC:
|
42C05 |
| MSC:
|
42C15 |
| idZBL:
|
Zbl 1249.42018 |
| idMR:
|
MR2978443 |
| DOI:
|
10.21136/MB.2012.142785 |
| . |
| Date available:
|
2012-04-18T23:56:58Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142785 |
| . |
| Reference:
|
[1] Okuyama, Y.: On the absolute Nörlund summability of orthogonal series.Proc. Japan Acad. 54 (1978), 113-118. Zbl 0409.42004, MR 0493132 |
| Reference:
|
[2] Okuyama, Y., Tsuchikura, T.: On the absolute Riesz summability of orthogonal series.Anal. Math. 7 (1981), 199-208. Zbl 0479.42008, MR 0635485, 10.1007/BF01908522 |
| Reference:
|
[3] Tanaka, M.: On generalized Nörlund methods of summability.Bull. Austral. Math. Soc. 19 (1978), 381-402. Zbl 0425.40004, MR 0536890, 10.1017/S0004972700008935 |
| Reference:
|
[4] Okuyama, Y.: On the absolute generalized Nörlund summability of orthogonal series.Tamkang J. Math. 33 (2002), 161-165. MR 1897504 |
| Reference:
|
[5] Flett, T. M.: On an extension of absolute summability and some theorems of Littlewood and Paley.Proc. London Math. Soc. 7 (1957), 113-141. Zbl 0109.04402, MR 0086912 |
| Reference:
|
[6] Flett, T. M.: Some more theorems concerning the absolute summability of Fourier series and power series.Proc. London Math. Soc. 8 (1958), 357-387. Zbl 0109.04502, MR 0102693 |
| Reference:
|
[7] Lal, S.: Approximation of functions belonging to the generalized Lipschitz Class by $C^{1}\cdot N_{p}$ summability method of Fourier series.Appl. Math. Comput. 209 (2009), 346-350. Zbl 1159.42302, MR 2493410, 10.1016/j.amc.2008.12.051 |
| . |
