Geodesic
Approximation Properties of Some Types of Linear Means in Space $L^{p(x)}_{2\pi}$
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 108-112.

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Approximative properties of Norlund $\mathcal{N}_{n}(f,x)$ and Riesz $\mathcal{R}_{n}(f,x)$ means for trigonometric Fourier series in Lebesgue space of variable exponent $L^{p(x)}_{2\pi}$ are considered. Under certain conditions on Norlund and Riesz summation methods it is proved that the estimates $\|f-\mathcal{N}_{n}\|_{p(\cdot)}\le CM\delta^{\alpha}$, $\|f-\mathcal{R}_{n}\|_{p(\cdot)}\le CM\delta^{\alpha}$ hold for $f\in \mathrm{Lip}_{p(\cdot)}(\alpha,M)$ ($0\alpha\le1$). 
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T. N. Shakh-Emirov. Approximation Properties of Some Types of Linear Means in Space $L^{p(x)}_{2\pi}$. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 108-112. http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a26/

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