Some new modified cosine sums and $L^{1}$-convergence of cosine trigonometric series
Archivum mathematicum, Tome 49 (2013) no. 1, pp. 43-50 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we introduce some new modified cosine sums and then using these sums we study $L^{1}$-convergence of trigonometric cosine series.
In this paper we introduce some new modified cosine sums and then using these sums we study $L^{1}$-convergence of trigonometric cosine series.
DOI : 10.5817/AM2013-1-43
Classification : 42A05, 42A20, 42A32
Keywords: $L^{1}$-convergence of trigonometric cosine series; new modified cosine sums; Dirichlet kernel
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Krasniqi, Xhevat Z. Some new modified cosine sums and $L^{1}$-convergence of cosine trigonometric series. Archivum mathematicum, Tome 49 (2013) no. 1, pp. 43-50. doi: 10.5817/AM2013-1-43

[1] Bary, N. K.: A treatise on trigonometric series. Pergamon Press, Oxford–London–New York–Paris–Frankfurt, 1964. | Zbl

[2] Fomin, G. A.: On linear methods for summing Fourier series. Math. Sbornik 66 (1964), 144–152. | MR

[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.

[4] Garret, W. J., Stanojević, Č. V.: On $L^1$–convergence of certain cosine sums. Proc. Amer. Math. Soc. 54 (1976), 101–105. | MR

[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. | MR | Zbl

[6] Kaur, J., Bhatia, S. S.: Integrability and $L^{1}$–convergence of certain cosine sums. Kyungpook Math. J. 47 (2007), 323–328. | MR | Zbl

[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. | DOI | MR | Zbl

[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

[9] Kaur, K.: On $L^1$–convergence of a modified sine sums. Electronic J. Geogr. Math. 14 (1) (2003).

[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

[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. | DOI | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | DOI | MR | Zbl

[15] Kumari, S., Ram, B.: $L^{1}$–convergence of certain trigonometric sums. Indian J. Pure Appl. Math. 20 (9) (1989), 908–914. | MR

[16] Leindler, L.: Additions to the Telyakovskiĭ class $S$. J. Inequal. Pure Appl. Math. 4 (2) (2003), 5, electronic only. | MR

[17] Ram, B.: Convergence of certain cosine sums in the metric space $L$. Proc. Amer. Math. Soc. 66 (1977), 258–260. | MR | Zbl

[18] Sidon, S.: Hinreichende Bedingungen für den Fourier-Charakter einer trigonometrischen Reihe. J. London Math. Soc. 14 (1939), 1528–160. | Zbl

[19] Singh, K., Kaur, K.: On $L^{1}$–convergence of certain generalized modified trigonometric sums. Mat. Vesnik 61 (3) (2009), 219–226. | MR | Zbl

[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

[21] Telyakovskiĭ, S. A.: On a sufficient condition of Sidon for integrability of trigonometric series. Math. Zametki 14 (1973), 317–328. | MR

[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

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