### Some sharp inequalities for approximations of periodic functions in $$$L_1$$$ space

#### Abstract

We provide sharp estimates of Jackson's inequalities type for the best $$$(\alpha, \beta)$$$-approximations in the space $$$L_1$$$ of periodic functions that are representable as the convolution of the kernel $$$K$$$ that does not increase the number of sign alternations with functions $$$\varphi \in C$$$, by means of convolutions of the kernel $$$K$$$ with the functions that are piecewise-constant in the intervals $$$\bigl( \frac{l \pi}{n}, \frac{(l+1)\pi}{n} \bigr)$$$.

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DOI: https://doi.org/10.15421/248701

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