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Title: Lim's theorems for multivalued mappings in CAT(0) spaces
Authors: S. Dhompongsa
A. Kaewkhao
B. Panyanak
Keywords: Mathematics
Issue Date: 15-Dec-2005
Abstract: Let X be a complete CAT(0) space. We prove that, if E is a nonempty bounded closed convex subset of X and T : E → K (X) a nonexpansive mapping satisfying the weakly inward condition, i.e., there exists p ∈ E such that αp⊕ (1 - α)Tx ⊂ IE(x) ∀x ∈ E, ∀α ∈ [0, 1], then T has a fixed point. In Banach spaces, this is a result of Lim [On asymptotic centers and fixed points of nonexpansive mappings, Canad. J. Math. 32 (1980) 421-430]. The related result for unbounded ℝ-trees is given. © 2005 Elsevier Inc. All rights reserved.
ISSN: 0022247X
Appears in Collections:CMUL: Journal Articles

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