CLASSES OF $L^1$-CONVERGENCE OF FOURIER SERIES

In this paper, wider classes of Fourier cosine series are introduced and found that $a_n \log n = o(1), ~ n \rightarrow \infty$ is a necessary and sufficient condition for $L^1$-convergence. Our results generalize the results obtained by A.N. Kolmogorov as well as R. Bala and B. Ram for cosine series while our new classes $\mathcal{JS}$ quasi convex and $\mathcal{JS}$ semi convex are the extensions of the classes quasi convex null sequence and semi convex respectively.