On Asymptotic Centers and Fixed Points of Nonexpansive Mappings

Lim, Teck-Cheong

Canadian journal of mathematics, Tome 32 (1980) no. 2, pp. 421-430

Résumé

Let X be a Banach space and B a bounded subset of X. For each x ∈ X, define R(x) = sup{‖x – y‖ : y ∈ B}. If C is a nonempty subset of X, we call the number R = inƒ{R(x) : x ∈ C} the Chebyshev radius of B in C and the set the Chebyshev center of B in C. It is well known that if C is weakly compact and convex, then and if, in addition, X is uniformly convex, then the Chebyshev center is unique; see e.g., [9].Let {Bα : α ∈ ∧} be a decreasing net of bounded subsets of X. For each x ∈ X and each α ∈ ∧, define

Détail

DOI : 10.4153/CJM-1980-033-5

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