ITERATED MEANS OF CONVEX-BODIES

Let K be a convex body in R(n) with polar K^. Let +p refer to Firey p or p-dot means. If 0 < lambda < 1,p greater-than-or-equal-to 1, K1 =lambda-K+(1-lambda)K^ and K(i+1) = lambda-K(i)+p(1 - lambda)K(i)^, for i greater-than-or-equal-to 1, then lim(i --> infinity) K(i) is the unit ball in R(n).