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On Asymptotic Centers and Fixed Points of Nonexpansive Mappings

Published online by Cambridge University Press:  20 November 2018

Teck-Cheong Lim
Teck-Cheong Lim*
Affiliation:
George Mason University, Fairfax, Virginia
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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

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 2 , February 1980 , pp. 421 - 430
Copyright
Copyright © Canadian Mathematical Society 1980

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