Lim's theorems for multivalued mappings in CAT(0) spaces
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 spa...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Journal |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=27744436289&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/62285 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| Summary: | 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. |
|---|