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

In this paper, the extensions of classes (S) over tilde, (C) over tilde and (B) over tildeV are made by defining the classes (S) over tilde (r), (C) over tilde (r) and (B) over tildeV(r), r = 0, 1, 2, . . . It is also shown that class (S) over tilde (r) is a subclass of (C) over tilde (r)boolean AND(B) over tildeV(r). Moreover, the results on L-1-convergence of r times differentiated trigonometric sine series have been obtained by considering the rth (r = 0, 1, 2, . . .) derivative of modified sine sum under the new extended class (C) over tilde (r)boolean AND(B) over tildeV(r).