New Characterization of Geodesic Convexity on Hadamard Manifolds with Applications |
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| Authors: | Li-wen Zhou Yi-bin Xiao Nan-jing Huang |
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| Affiliation: | 1.School of Sciences,Southwest Petroleum University,Chengdu,People’s Republic of China;2.School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu,People’s Republic of China;3.Department of Mathematics,Sichuan University,Chengdu,People’s Republic of China |
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| Abstract: | 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. |
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