  In this paper, we investigate the inequality \begin{equation*} \left\Vert
f(\cdot +h)\right\Vert_{p\left( \cdot \right) }\leq A\left\Vert
f\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 the
variable exponent $p$.
