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Title: Fixed Points of Nonexpansive Mappings on Weak and Weak-Star Compact Convex Sets in Banach Spaces
Contributor(s): Taviri, Raka (author); Sims, B (supervisor)
Conferred Date: 1986
Copyright Date: 1985
Open Access: Yes
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Abstract: Let X be a Banach space, K a nonempty bounded closed convex subset of X and T a nonexpansive selfmapping of K. The purpose of this thesis is to investigate the following question: What further assumptions (of a geometrical nature) on K (or X) can we make to ensure that there exists a point x in K for which Tx = x? Such points in K are called fixed points of T in K. X is then said to have the fixed point property (FPP) if for every nonempty bounded-closed convex subset K of X, each nonexpansive selfmapping T of K has a fixed point. This, together with the following two properties, will be the subject of our subsequent investigation. The weak fixed point property (w-FPP): For every nonempty weak compact convex subset K of X and each nonexpansive selfmapping T: K → K, there exists x ∈ K with Tx=x; and in the case of a dual space X*. The weak-star fixed point property (w*-FPP): For every nonempty weak-star compact convex subset K of X* and each nonexpansive self-mapping T: K→ K, there exists x ∈ K with Tx=x.
Publication Type: Thesis Masters Research
Rights Statement: Copyright 1985 - Raka Taviri
HERDC Category Description: T1 Thesis - Masters Degree by Research
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