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.
Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure.
CASINI, EMANUELE GIUSEPPE;
1985-01-01
Abstract
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.
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