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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 [11] for Hubert spaces, by Browder [2] for spaces having weakly continuous duality mapping, and by Lami Dozo [7] for spaces satisfying OpiaPs condition. Lami Dozo's result is also generalized by Assad and Kirk [1]. By making use of Edelstein's asymptotic center [4], [5], we are able to prove Theorem 1. Let C be a closed convex subset of a uniformly convex Banach space and let {wj be a bounded sequence in C. The asymptotic center x of {wj in (or with respect to) C is the unique point in C such that

A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space