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In this paper, the problem of -convergence of Fourier series with quasi-monotone coefficients is handled by using the -mean. Also, an example is given about the Fourier series of a signal (function) and its mean. [ABSTRACT FROM AUTHOR]

Asymptotic expansions in powers of δ as δ → +∞ of the series where β ∈ ℤ, α, a, b > 0, and r ∈ ℂ, while Q is an algebraic polynomial satisfying the condition Q(0) = 0, are obtained. In special cases, these series arise from the approximation of periodic differentiable functions by the Riesz and Cesàro means. [ABSTRACT FROM AUTHOR]

We establish the order of approximation by Riesz means of the Fourier series in a multiplicative system of a class of functions with given majorant of the sequence of best approximations. In some cases, approximations by Riesz means and best approximations are considered in a specific space, but, in other cases, approximations by Riesz means are considered in spaces with a stronger norm. [ABSTRACT FROM AUTHOR]

A theorem on $$ |\overline N ,p_n |_k $$-summability factors of infinite series is proved under weaker conditions. A new result concerning the | C, 1| k-summability factors is also obtained. [ABSTRACT FROM AUTHOR]