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A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space
Bulletin of the American Mathematical Society
Let C be a nonempty weakly compact convex subset of a Banach space X, and ^(C) be the family of nonempty compact subsets of C equipped with the Hausdorff metric. Let T: C-^€(C) be a nonexpansive mapping, i.e. for each x, y e C, H(T(x) 9 T(y))£\\x-y\\ 9 where H (A, B) denotes the Hausdorff distance between A and B. A point x e C is called a fixed point of T if x e Tx. Fixed point theorems for such mappings T have been established by Mar kin  for Hubert spaces, by Browder  for spacesdoi:10.1090/s0002-9904-1974-13640-2 fatcat:xinqalc2prechlhe4fw7tlc6du