Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure.

Let K be a closed convex and bounded subset of a Banach space X. Suppose T:X ! X is a
uniformly Lipschitzian mapping, i.e. kTnx−Tnyk
kx−yk for all x, y 2 K and n = 1, 2, · · ·.
We prove a fixed point result for a space having uniform
normal structure. These are spaces for which N(X) = sup{r(C, coC): diamC = 1} < 1, where
r(C, coC) denotes the Chebyshev radius of the set C with respect to its convex closure.