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In this paper, wider classes of Fourier cosine series are introduced and found that an log n = o(1), n → ∞ is a necessary and sufficient condition for L1- 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 J S quasi convex and J S semi convex are the extensions of the classes quasi convex null sequence and semi convex respectively.
Gill et al. (Tue,) studied this question.
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