New Characterization of Geodesic Convexity on Hadamard Manifolds with Applications

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• 作者：Li-wen Zhou ; Yi-bin Xiao ; Nan-jing Huang
• 关键词：Hadamard manifold ; Geodesic convex hull ; Geodesic convex combination ; S ; KKM theorem ; Fixed point theorem
• 刊名：Journal of Optimization Theory and Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：172
• 期：3
• 页码：824-844
• 全文大小：
• 刊物主题：Calculus of Variations and Optimal Control; Optimization; Optimization; Theory of Computation; Applications of Mathematics; Engineering, general; Operation Research/Decision Theory;
• 出版者：Springer US
• ISSN：1573-2878
• 卷排序：172

文摘

In this paper, some new results, concerned with the geodesic convex hull and geodesic convex combination, are given on Hadamard manifolds. An S-KKM theorem on a Hadamard manifold is also given in order to generalize the KKM theorem. As applications, a Fan–Browder-type fixed point theorem and a fixed point theorem for the a new mapping class are proved on Hadamard manifolds.