Some new modified cosine sums and $L^1$-convergence of cosine trigonometric series

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1. Bary, N. K., A treatise on trigonometric series, Pergamon Press, Oxford–London–New York–Paris–Frankfurt, 1964. (1964) Zbl0129.28002
2. Fomin, G. A., On linear methods for summing Fourier series, Math. Sbornik 66 (1964), 144–152. (1964) MR0168988
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. (1975) 
4. Garret, W. J., Stanojević, Č. V., On $L^1$–convergence of certain cosine sums, Proc. Amer. Math. Soc. 54 (1976), 101–105. (1976) MR0394002
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. (2002) Zbl1019.42002MR1926327
6. Kaur, J., Bhatia, S. S., Integrability and $L^1$–convergence of certain cosine sums, Kyungpook Math. J. 47 (2007), 323–328. (2007) Zbl1143.42300MR2413939
7. Kaur, J., Bhatia, S. S., 10.1134/S1995080210030121, Lobachevskii J. Math. 31 (3) (2010), 290–294. (2010) Zbl1256.42007MR2720651DOI10.1134/S1995080210030121
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. (2012) MR3057813
9. Kaur, K., On $L^1$–convergence of a modified sine sums, Electronic J. Geogr. Math. 14 (1) (2003). (2003) 
10. Kaur, K., Integrability and $Lsp1$–convergence of Rees–Stanojevic sums with generalized semi–convex coefficients of non–integral orders, Arch. Math. (Brno) 41 (4) (2005), 423–437. (2005) MR2195495
11. Kaur, K., Bhatia, S. S., 10.1155/S0161171202012942, Int. J. Math. Math. Sci. 30 (11) (2002), 645–650. (2002) Zbl1010.42017MR1916824DOI10.1155/S0161171202012942
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. (2004) Zbl1051.42004MR2065543
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. (2009) Zbl1208.42002MR2524696
14. Krasniqi, Xh. Z., 10.4418/2010.65.2.3, , Matematiche 65 (2) (2010), 25–32. (2010) Zbl1239.42004MR2802066DOI10.4418/2010.65.2.3
15. Kumari, S., Ram, B., $L^1$–convergence of certain trigonometric sums, Indian J. Pure Appl. Math. 20 (9) (1989), 908–914. (1989) MR1015638
16. Leindler, L., Additions to the Telyakovskiĭ class $S$, J. Inequal. Pure Appl. Math. 4 (2) (2003), 5, electronic only. (2003) MR1994248
17. Ram, B., Convergence of certain cosine sums in the metric space $L$, Proc. Amer. Math. Soc. 66 (1977), 258–260. (1977) Zbl0367.42011MR0461013
18. Sidon, S., Hinreichende Bedingungen für den Fourier-Charakter einer trigonometrischen Reihe, J. London Math. Soc. 14 (1939), 1528–160. (1939) Zbl0021.40301
19. Singh, K., Kaur, K., On $L^1$–convergence of certain generalized modified trigonometric sums, Mat. Vesnik 61 (3) (2009), 219–226. (2009) Zbl1265.42012MR2546612
20. Singh, N., Sharma, K. M., Convergence of certain cosine sums in the metric space $L$, Proc. Amer. Math. Soc. 75 (1978), 117–120. (1978) MR0503543
21. Telyakovskiĭ, S. A., On a sufficient condition of Sidon for integrability of trigonometric series, Math. Zametki 14 (1973), 317–328. (1973) MR0328456
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. (2002) Zbl0999.42004