• L1-CONVERGENCE OF DERIVATIVE OF FOURIER SERIES USING MODIFIED SUMS

KARANVIR SINGH*, KANAK MODI

Abstract


In this paper we discuss the L1-convergence of the r-th derivative of Fourier series using modified trigonometric sums introduced by Rees and Stanojevic [15] and by Kumari and Ram [12]. It is shown that results concerning L1-convergence of r-th derivative of trigonometric series can be better established using modified trigonometric sums as compared to classical partial sums. Previously obtained results in this direction by Bhatia and Ram [3] and Kaur and Bhatia [9] have been generalised.


Keywords


L1−convergence, quasi-convex, modified cosine sums, Dirichlet's kernel, Fezer kernel.

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