Approximation by $\Omega$-continued fractions

Let $x\in (0,1)$ be a real number, $x=[0;\varepsilon_1/b_1,\ldots,\varepsilon_1/b_n,\ldots]$ be its expansion in $\Omega$-continued fraction. Let $A_n/B_n$ be its nth convergent and $\Upsilon_n=\Upsilon_n(x)=B^2_n|x -A_n/B_n|$. In this note we prove the analog of the classical theorems by Borel and Hurwitz on the quality of the approximations for $\Omega$-continued fractions: $\min(\Upsilon_{n-1}, \Upsilon_{n},\Upsilon_{n+1})\le 1/\sqrt{5}$. The result is best possible.