Extensions of Móricz Classes and Convergence of Trigonometric Sine Series in L 1 -Norm

Sandeep Kaur Chouhan, Jatinderdeep Kaur and Satvinder Singh Bhatia
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Sandeep Kaur Chouhan: Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India
Jatinderdeep Kaur: Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India
Satvinder Singh Bhatia: Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India

Mathematics, 2018, vol. 6, issue 12, 1-8

Abstract: 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 .

Keywords: Dirichlet kernel; L 1 -convergence; modified sine sum (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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