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

Mathematics

卷:6

SatvinderSingh Bhatia¹  Jatinderdeep Kaur¹  SandeepKaur Chouhan¹ 

[1] Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India;

关键词: Dirichlet kernel;    L¹-convergence;    modified sine sum;   

DOI  :  10.3390/math6120292

来源: DOAJ

【 摘 要 】

In this paper, the extensions of classes $\tilde{S},\tilde{C}$ and $\tilde{B}V$ are made by defining the classes ${\tilde{S}}_r$ , ${\tilde{C}}_r$ and $\tilde{B}{V}_r$ , $r=0,1,2,\dots$ It is also shown that class ${\tilde{S}}_r$ is a subclass of ${\tilde{C}}_r{\displaystyle \cap \tilde{B}{V}_r}$ . Moreover, the results on $L^1$ -convergence of r times differentiated trigonometric sine series have been obtained by considering the $r^{th}(r=0,1,2,\dots )$ derivative of modified sine sum under the new extended class ${\tilde{C}}_r{\displaystyle \cap \tilde{B}{V}_r}$ .

【 授权许可】

Unknown