# CONVERGENCE OF NEW MODIFIED TRIGONOMETRIC SUMS IN THE METRIC SPACE L

Volume 1, Issue 3, pp 179-188
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### Authors

JATINDERDEEP KAUR - School of Mathematics & Computer Applications, Thapar University Patiala(Pb.)-147004, INDIA.. S.S. BHATIA - School of Mathematics & Computer Applications, Thapar University Patiala(Pb.)-147004, INDIA..

### Abstract

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.

### Share and Cite

##### ISRP Style

JATINDERDEEP KAUR, S.S. BHATIA, CONVERGENCE OF NEW MODIFIED TRIGONOMETRIC SUMS IN THE METRIC SPACE L, Journal of Nonlinear Sciences and Applications, 1 (2008), no. 3, 179-188

##### AMA Style

KAUR JATINDERDEEP, BHATIA S.S., CONVERGENCE OF NEW MODIFIED TRIGONOMETRIC SUMS IN THE METRIC SPACE L. J. Nonlinear Sci. Appl. (2008); 1(3):179-188

##### Chicago/Turabian Style

KAUR , JATINDERDEEP, BHATIA, S.S.. "CONVERGENCE OF NEW MODIFIED TRIGONOMETRIC SUMS IN THE METRIC SPACE L." Journal of Nonlinear Sciences and Applications, 1, no. 3 (2008): 179-188

### Keywords

• $L^1$-convergence
• Dirichlet kernel
• Fejer kernel
• monotone sequence.

•  42A20
•  42A32

### References

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