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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th-cmuir.6653943832-609872018-09-10T04:06:51Z Best approximation in ℝ-trees W. A. Kirk B. Panyanak Computer Science Mathematics 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. 2018-09-10T04:02:28Z 2018-09-10T04:02:28Z 2007-05-01 Journal 15322467 01630563 2-s2.0-34249098113 10.1080/01630560701348517 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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Computer Science Mathematics |
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Computer Science Mathematics W. A. Kirk B. Panyanak Best approximation in ℝ-trees |
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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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Journal |
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W. A. Kirk B. Panyanak |
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W. A. Kirk B. Panyanak |
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W. A. Kirk |
| title |
Best approximation in ℝ-trees |
| title_short |
Best approximation in ℝ-trees |
| title_full |
Best approximation in ℝ-trees |
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Best approximation in ℝ-trees |
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Best approximation in ℝ-trees |
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best approximation in ℝ-trees |
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2018 |
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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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