Convergence of subsets of a complete geodesic space with curvature bounded above

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• 作者：Yasunori Kimura^a ; ^{yasunori@is.sci.toho-u.ac.jp} ; Kenzi Satô ; ^b ; ^{kenzi@eng.tamagawa.ac.jp}
• 关键词：49J53
• 刊名：Nonlinear Analysis
• 出版年：2012
• 期刊代码：43_0362546x
• 类别：mt
• 出版时间：September, 2012
• 卷：75
• 期：13
• 页码：5079-5085
• 文件大小：224 K

摘要

We consider a notion of set-convergence in a Hadamard space recently defined by Kimura and extend it to that in a complete geodesic space with curvature bounded above by a positive number. We obtain its equivalent condition by using the corresponding sequence of metric projections. We also discuss the Kadec-Klee property on such spaces and interaction among this set-convergence having different curvatures.