Weighted approximations by means of entire functions of exponential type

We study the approximation of continuous real functions $f(x)=O((1+|x|)^\alpha)(|x|\to\infty$, $\sigma\ge0)$ by means of entire functions of exponential type in some metric of Hausdorff type. We generalize a theorem due to N. I. Akhiezer concerning uniform weighted approximations.