New Characterization of Geodesic Convexity on Hadamard Manifolds with Applications

Li-wen Zhou (), Yi-bin Xiao () and Nan-jing Huang ()
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Li-wen Zhou: Southwest Petroleum University
Yi-bin Xiao: University of Electronic Science and Technology of China
Nan-jing Huang: Sichuan University

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 3, No 6, 824-844

Abstract: 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.

Keywords: Hadamard manifold; Geodesic convex hull; Geodesic convex combination; S-KKM theorem; Fixed point theorem; 49J40; 47J20 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-016-1012-0

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