Approximation Properties of Some Types of Linear Means in Space $L^{p(x)}_{2\pi}$

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 $f\in \mathrm{Lip}_{p(\cdot)}(\alpha,M)$ ($0<\alpha\le1$).