Best approximation in ℝ-trees
An ℝ-tree is a geodesic space for which there is a unique arc joining any two of its points, and this arc is a metric segment. We give a constructive proof of the following "best approximation" theorem in such spaces. Suppose X is a closed convex and geodesically bounded subset of an ℝ-tre...
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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=34249098113&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/60987 |
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| Institution: | Chiang Mai University |
| Summary: | An ℝ-tree is a geodesic space for which there is a unique arc joining any two of its points, and this arc is a metric segment. We give a constructive proof of the following "best approximation" theorem in such spaces. Suppose X is a closed convex and geodesically bounded subset of an ℝ-tree H, and suppose T:X2H is a multivalued upper semicontinuous mapping whose values are nonempty closed convex subsets of X. Then there exists a point x0X such that [image omitted] We also give a topological version of the above theorem in a more abstract setting, and we prove a KKM theorem for geodesically bounded ℝ-trees. |
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