On stability of Möbius transformations in the class of mappings with bounded distortion

Let $f\colon B(0,1)\to\mathbb{R}^n$ be a mapping with bounded distortion, and $K(x,f)$ be the distortion coefficient of the mapping $f$ at the point $x$. It is proved that if the function $K(x,f)$ is close to 1 in some integral sense, then the mapping $f$ is close to a Möbius transformation.