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Extensions of Móricz Classes and Convergence of Trigonometric Sine Series in L1-Norm

Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India
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Mathematics 2018, 6(12), 292; https://doi.org/10.3390/math6120292
Received: 11 September 2018 / Revised: 14 November 2018 / Accepted: 21 November 2018 / Published: 29 November 2018
(This article belongs to the Special Issue Harmonic Analysis)
In this paper, the extensions of classes S ˜ ,   C ˜ and B ˜ V are made by defining the classes S ˜ r , C ˜ r and B ˜ V r , r = 0 , 1 , 2 , It is also shown that class S ˜ r is a subclass of C ˜ r B ˜ V r . Moreover, the results on L 1 -convergence of r times differentiated trigonometric sine series have been obtained by considering the r t h ( r = 0 , 1 , 2 , ) derivative of modified sine sum under the new extended class C ˜ r B ˜ V r . View Full-Text
Keywords: Dirichlet kernel; L1-convergence; modified sine sum Dirichlet kernel; L1-convergence; modified sine sum
MDPI and ACS Style

Chouhan, S.K.; Kaur, J.; Bhatia, S.S. Extensions of Móricz Classes and Convergence of Trigonometric Sine Series in L1-Norm. Mathematics 2018, 6, 292.

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