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...
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th-cmuir.6653943832-622852018-09-11T09:25:07Z Lim's theorems for multivalued mappings in CAT(0) spaces S. Dhompongsa A. Kaewkhao B. Panyanak Mathematics 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. 2018-09-11T09:25:07Z 2018-09-11T09:25:07Z 2005-12-15 Journal 0022247X 2-s2.0-27744436289 10.1016/j.jmaa.2005.03.055 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=27744436289&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/62285 |
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Mathematics S. Dhompongsa A. Kaewkhao B. Panyanak Lim's theorems for multivalued mappings in CAT(0) spaces |
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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. |
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Journal |
| author |
S. Dhompongsa A. Kaewkhao B. Panyanak |
| author_facet |
S. Dhompongsa A. Kaewkhao B. Panyanak |
| author_sort |
S. Dhompongsa |
| 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 |
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2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=27744436289&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/62285 |
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