Approximation of the function |sin x| s by the partial sums of the trigonmometric rational fourier series

In the present article, the approximation of the function |sin x| s by the partial sums of the rational trigonometric Fourier series is considered. An integral representation, uniform and point estimates for the above-mentioned approximation were obtained. Based on them, several special cases of the selection of poles were studied. In the case of the approximation by the partial sums of the polynomial trigonometric Fourier series, an asymptotic equality was found. A detailed study is made of a fixed number of geometrically different poles.

On degree of approximation of Fourier series of functions in Besov space using Norlund meanIn the present article, we have established a result on degree of approximation of function in the Besov space by (N; rn)- mean of Trigonometric Fourier series

In the present article, we have established a result on degree of approximation of function in the Besov space by (N; rn)- mean of Trigonometric Fourier series

A note on the strong summability of two-dimensional Walsh–Fourier series

In this paper, we investigate the strong summability of two-dimensional Walsh–Fourier series obtained in [F. Weisz, Strong convergence theorems for two-parameter Walsh–Fourier and trigonometric-Fourier series, Studia Math. 117 1996, 2, 173–194] (see Theorem W) and prove the sharpness of this result.