Stability of isodiametric problem solution in the Minkowski geometry

The theorem is proved: if $(D_B(X)/2)^n-V_B(X)/V_B(B_1)\le\varepsilon$, $0\le\varepsilon$, $V_B(X)=V_B(B_1)$, then $\delta_B(X,B_1)\le2\varepsilon^{1/n}$, where $X$ – convex body in $n$-dimensional space of Minkowski $\tilde M^n$, $B$ – normed body $\tilde M^n$, $B_1=B\cap(-B)$, $V_B(X)$ – diameter $X$, $V_B(X)$ – volume $X$, $\delta_B(X,B_1)$ – deflection of bodies $X$ and $B_1$ in $\tilde M^n$.