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In this paper, we investigate the inequality \begin{equation*} \left\Vertf(\cdot +h)\right\Vert_{p\left( \cdot \right) }\leq A\left\Vertf\right\Vert_{p\left( \cdot \right) },\quad h\in \mathbb{R}^{n}, A>0\end{equation*} under some suitable assumptions on the function $f$ and thevariable exponent $p$.

Restricted boundedness of translation operators on variable Lebesgue spaces