  It is shown that for any sufficiently regular even Minkowski valuation $\Phi$
which is homogeneous and intertwines rigid motions, and for any convex body $K$
in a smooth neighborhood of the unit ball, there exists a sequence of positive
numbers $(\gamma_m)_{m=1}^\infty$ such that $(\gamma_m\Phi^m K)_{m=1}^\infty$
converges to the unit ball with respect to the Hausdorff metric.
