Further results on \(L^{1}\)-convergence of some modified complex trigonometric sums

Xhevat Z. Krasniqi

doi:10.33993/jnaat442-1072

Authors

Xhevat Z. Krasniqi University of Prishtina ”Hasan Prishtina”, Albania

DOI:

https://doi.org/10.33993/jnaat442-1072

Keywords:

\(L^1\)-convergence, null sequence, trigonometric series, modified sums

Abstract views: 280

Abstract

In this paper we have defined a new class of numerical sequences, which tend to zero, briefly denoted by \(\mathbb{K}^{2}\).
Moreover, employing such class of numerical sequences we have studied \(L^{1}\)-convergence of some modified complex trigonometric sums introduced previously by others.

Downloads

Download data is not yet available.

References

B. Ram, Convergence of certain cosine sums in the metric space L, Proc. Amer. Math. Soc., 66 (1977), pp. 258–260, http://doi.org/10.2307/2040941 DOI: https://doi.org/10.1090/S0002-9939-1977-0461013-4

B. Ram, Integrability of Ress-Stanojevic sums, Acta Sci. Math., 42 (1980), pp. 153–155.

C. S. Rees and C. V. Stanojevic, Necessary and sufficient condition for intergrability of certain cosine sums, J. Math. Anal. Appl., 43 (1973), pp. 579–586, http://doi.org/10.1016/0022-247X(73)90278-3 DOI: https://doi.org/10.1016/0022-247X(73)90278-3

L. Leindler, Additions to the Telyakovski class S, J. Ineq. Pure and Appl. Math., 4 (2003) Art. 35.

N. K. Bary, A treatise on trigonometric series (London: Pergamon Press) Vol.II, 1964.

S. A. Telyakovski , On a sufficient condition of Sidon for integrability of trigonometric series, Math. Zametki, (in Russian) 14 (1973), pp. 317–328. DOI: https://doi.org/10.1007/BF01147448

S. S. Bhatia and B. Ram, The extensions of the F. Moricz’s theorems, Proc. Amer. Math. Soc. 124 (1996), no. 6, pp. 1821–904, http://doi.org/10.1090/S0002-9939-96-03212-1 DOI: https://doi.org/10.1090/S0002-9939-96-03212-1

S. Kumari and B. Ram, L Appl. Math. 20 (9), 908–914, 1989. DOI: https://doi.org/10.1137/0520061

J. Kaur and S. S. Bhatia, Convergence of modified complex trigonometric sums in the metric space L, Lobachevskii J. Math., 31 (2010), No. 3, pp. 290–294, http://doi.org/10.1134/S1995080210030121 DOI: https://doi.org/10.1134/S1995080210030121

J. Kaur and S. S. Bhatia, A class of L Southeast Asian Bull. Math., 36 (6) (2012), pp. 831–836.

K. Kaur, S. S. Bhatia and B. Ram, Integrability and L sums, Georgian. Math. J. 11 (1) (2004), pp. 99–104, http://doi.org/10.1515/GMJ.2004.99 DOI: https://doi.org/10.1515/GMJ.2004.99

T. Kano, Coefficients of some trigonometric series, J. Fac. Sci. Shinshu Univ., 3 (1968), pp. 153–162.

Xh. Z. Krasniqi, L Mat., Tomus XXII (2015), No. 1, pp. 41–46.

Xh. Z. Krasniqi, Some new modified cosine sums and L metric series, Arch. Math. (Brno), Tomus 49 (2013), pp. 43–50. DOI: https://doi.org/10.5817/AM2013-1-43

Xh. Z. Krasniqi, On L the class K, Matematiche (Catania), Vol. LXV–Fasc. II (2010), pp. 25–32, http://doi.org/10.4418/2010.65.2.3

Z. Tomovski, On a theorem of S. S. Bhatia and B. Ram, Math. Commun, 8, 187–193, 2003