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..
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.
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
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
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
