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: | Article |
| Language: | English |
| Published: |
2014
|
| Online Access: | http://www.scopus.com/inward/record.url?eid=2-s2.0-27744436289&partnerID=40&md5=7a28ec88ae27b3f21b25105f4a692f49 http://cmuir.cmu.ac.th/handle/6653943832/4891 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| Language: | English |
| id |
th-cmuir.6653943832-4891 |
|---|---|
| record_format |
dspace |
| spelling |
th-cmuir.6653943832-48912014-08-30T02:55:55Z Lim's theorems for multivalued mappings in CAT(0) spaces Dhompongsa S. Kaewkhao A. Panyanak B. 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. 2014-08-30T02:55:55Z 2014-08-30T02:55:55Z 2005 Article 0022247X 10.1016/j.jmaa.2005.03.055 http://www.scopus.com/inward/record.url?eid=2-s2.0-27744436289&partnerID=40&md5=7a28ec88ae27b3f21b25105f4a692f49 http://cmuir.cmu.ac.th/handle/6653943832/4891 English |
| institution |
Chiang Mai University |
| building |
Chiang Mai University Library |
| country |
Thailand |
| collection |
CMU Intellectual Repository |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Dhompongsa S. Kaewkhao A. Panyanak B. |
| spellingShingle |
Dhompongsa S. Kaewkhao A. Panyanak B. Lim's theorems for multivalued mappings in CAT(0) spaces |
| author_facet |
Dhompongsa S. Kaewkhao A. Panyanak B. |
| author_sort |
Dhompongsa S. |
| title |
Lim's theorems for multivalued mappings in CAT(0) spaces |
| title_short |
Lim's theorems for multivalued mappings in CAT(0) spaces |
| title_full |
Lim's theorems for multivalued mappings in CAT(0) spaces |
| title_fullStr |
Lim's theorems for multivalued mappings in CAT(0) spaces |
| title_full_unstemmed |
Lim's theorems for multivalued mappings in CAT(0) spaces |
| title_sort |
lim's theorems for multivalued mappings in cat(0) spaces |
| publishDate |
2014 |
| url |
http://www.scopus.com/inward/record.url?eid=2-s2.0-27744436289&partnerID=40&md5=7a28ec88ae27b3f21b25105f4a692f49 http://cmuir.cmu.ac.th/handle/6653943832/4891 |
| _version_ |
1681420322369175552 |