Geodesic
CONVERGENCE OF NEW MODIFIED TRIGONOMETRIC SUMS IN THE METRIC SPACE L
KAUR , JATINDERDEEP1 ; BHATIA, S.S.1
1 School of Mathematics & Computer Applications, Thapar University Patiala(Pb.)-147004, INDIA.
Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 3, p. 179-188.

Voir la notice de l'article provenant de la source International Scientific Research Publications

We introduce here new modified cosine and sine sums as $\frac{a_0}{ 2} + \sum^n_{ k=1} \sum^n_{ j=k} \triangle(a_j \cos jx)$ and $ \sum^n_{ k=1} \sum^n_{ j=k} \triangle(a_j \sin jx)$ and study their integrability and $L^1$-convergence. The $L^1$-convergence of cosine and sine series have been obtained as corollary. In this paper, we have been able to remove the necessary and sufficient condition $a_k \log k = o(1)$ as $k \rightarrow\infty$ for the $L^1$-convergence of cosine and sine series.
DOI : 10.22436/jnsa.001.03.06
Classification : 42A20, 42A32
Keywords: \(L^1\)-convergence, Dirichlet kernel, Fejer kernel, monotone sequence.

KAUR , JATINDERDEEP 1 ; BHATIA, S.S. 1

1 School of Mathematics & Computer Applications, Thapar University Patiala(Pb.)-147004, INDIA. 
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KAUR  , JATINDERDEEP; BHATIA,  S.S. CONVERGENCE OF NEW MODIFIED TRIGONOMETRIC SUMS IN THE METRIC SPACE L. Journal of nonlinear sciences and its applications, Tome 1 (2008) no. 3, p. 179-188. doi : 10.22436/jnsa.001.03.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.001.03.06/

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