| Title:
|
Some new modified cosine sums and $L^{1}$-convergence of cosine trigonometric series (English) |
| Author:
|
Krasniqi, Xhevat Z. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2013 |
| Pages:
|
43-50 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce some new modified cosine sums and then using these sums we study $L^{1}$-convergence of trigonometric cosine series. (English) |
| Keyword:
|
$L^{1}$-convergence of trigonometric cosine series |
| Keyword:
|
new modified cosine sums |
| Keyword:
|
Dirichlet kernel |
| MSC:
|
42A05 |
| MSC:
|
42A20 |
| MSC:
|
42A32 |
| idZBL:
|
Zbl 06321147 |
| idMR:
|
MR3073015 |
| DOI:
|
10.5817/AM2013-1-43 |
| . |
| Date available:
|
2013-05-28T13:30:30Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143299 |
| . |
| Reference:
|
[1] Bary, N. K.: A treatise on trigonometric series.Pergamon Press, Oxford–London–New York–Paris–Frankfurt, 1964. Zbl 0129.28002 |
| Reference:
|
[2] Fomin, G. A.: On linear methods for summing Fourier series.Math. Sbornik 66 (1964), 144–152. MR 0168988 |
| Reference:
|
[3] Garret, W. J., Stanojević, Č. V.: On integrability and $L^1$–convergence of certain cosine sums.Notices, Amer. Math. Soc. 22 (1975), A–166. |
| Reference:
|
[4] Garret, W. J., Stanojević, Č. V.: On $L^1$–convergence of certain cosine sums.Proc. Amer. Math. Soc. 54 (1976), 101–105. MR 0394002 |
| Reference:
|
[5] Hooda, N., Ram, B., Bhatia, S. S.: On $L^1$–convergence of a modified cosine sum.Soochow J. of Math. 28 (3) (2002), 305–310. Zbl 1019.42002, MR 1926327 |
| Reference:
|
[6] Kaur, J., Bhatia, S. S.: Integrability and $L^{1}$–convergence of certain cosine sums.Kyungpook Math. J. 47 (2007), 323–328. Zbl 1143.42300, MR 2413939 |
| Reference:
|
[7] Kaur, J., Bhatia, S. S.: Convergence of modified complex trigonometric sums in the metric space $L$.Lobachevskii J. Math. 31 (3) (2010), 290–294. Zbl 1256.42007, MR 2720651, 10.1134/S1995080210030121 |
| Reference:
|
[8] Kaur, J., Bhatia, S. S.: A class of $L^1$–convergence of new modified cosine sums.Southeast Asian Bull. Math. 36 (2012), 831–836. MR 3057813 |
| Reference:
|
[9] Kaur, K.: On $L^1$–convergence of a modified sine sums.Electronic J. Geogr. Math. 14 (1) (2003). |
| Reference:
|
[10] Kaur, K.: Integrability and $L sp 1$–convergence of Rees–Stanojevic sums with generalized semi–convex coefficients of non–integral orders.Arch. Math. (Brno) 41 (4) (2005), 423–437. MR 2195495 |
| Reference:
|
[11] Kaur, K., Bhatia, S. S.: Integrability and $L^{1}$–convergence of Ress–Stanojević sums with generalized semi–convex coefficients.Int. J. Math. Math. Sci. 30 (11) (2002), 645–650. Zbl 1010.42017, MR 1916824, 10.1155/S0161171202012942 |
| Reference:
|
[12] Kaur, K., Bhatia, S. S., Ram, B.: Integrability and $L^{1}$–convergence of modified sine sums.Georgian Math. J. 11 (1) (2004), 99–104. Zbl 1051.42004, MR 2065543 |
| Reference:
|
[13] Krasniqi, Xh. Z.: A note on $L^1$–convergence of the sine and cosine trigonometric series with semi–convex coefficients.Int. J. Open Probl. Comput. Sci. Math. 2 (2) (2009), 231–239. Zbl 1208.42002, MR 2524696 |
| Reference:
|
[14] Krasniqi, Xh. Z.: On $L^1$–convergence of Rees–Stanojević’s sums with coefficients from the class K., Matematiche 65 (2) (2010), 25–32. Zbl 1239.42004, MR 2802066, 10.4418/2010.65.2.3 |
| Reference:
|
[15] Kumari, S., Ram, B.: $L^{1}$–convergence of certain trigonometric sums.Indian J. Pure Appl. Math. 20 (9) (1989), 908–914. MR 1015638 |
| Reference:
|
[16] Leindler, L.: Additions to the Telyakovskiĭ class $S$.J. Inequal. Pure Appl. Math. 4 (2) (2003), 5, electronic only. MR 1994248 |
| Reference:
|
[17] Ram, B.: Convergence of certain cosine sums in the metric space $L$.Proc. Amer. Math. Soc. 66 (1977), 258–260. Zbl 0367.42011, MR 0461013 |
| Reference:
|
[18] Sidon, S.: Hinreichende Bedingungen für den Fourier-Charakter einer trigonometrischen Reihe.J. London Math. Soc. 14 (1939), 1528–160. Zbl 0021.40301 |
| Reference:
|
[19] Singh, K., Kaur, K.: On $L^{1}$–convergence of certain generalized modified trigonometric sums.Mat. Vesnik 61 (3) (2009), 219–226. Zbl 1265.42012, MR 2546612 |
| Reference:
|
[20] Singh, N., Sharma, K. M.: Convergence of certain cosine sums in the metric space $L$.Proc. Amer. Math. Soc. 75 (1978), 117–120. MR 0503543 |
| Reference:
|
[21] Telyakovskiĭ, S. A.: On a sufficient condition of Sidon for integrability of trigonometric series.Math. Zametki 14 (1973), 317–328. MR 0328456 |
| Reference:
|
[22] Tomovski, Ž.: Some results on $L^1$–approximation of the $r$–th derivative of Fourier series.J. Inequal. Pure Appl. Math. 1 (2002), 11, electronic only. Zbl 0999.42004 |
| . |
