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New Characterization of Geodesic Convexity on Hadamard Manifolds with Applications

Author

Listed:
  • Li-wen Zhou

    (Southwest Petroleum University)

  • Yi-bin Xiao

    (University of Electronic Science and Technology of China)

  • Nan-jing Huang

    (Sichuan University)

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.

Suggested Citation

  • Li-wen Zhou & Yi-bin Xiao & Nan-jing Huang, 2017. "New Characterization of Geodesic Convexity on Hadamard Manifolds with Applications," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 824-844, March.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-016-1012-0
    DOI: 10.1007/s10957-016-1012-0
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    References listed on IDEAS

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    1. O. Ferreira & L. Pérez & S. Németh, 2005. "Singularities of Monotone Vector Fields and an Extragradient-type Algorithm," Journal of Global Optimization, Springer, vol. 31(1), pages 133-151, January.
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    Cited by:

    1. Orizon P. Ferreira & Sándor Z. Németh & Jinzhen Zhu, 2024. "Convexity of Sets and Quadratic Functions on the Hyperbolic Space," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 421-455, July.
    2. Li-wen Zhou & Nan-jing Huang, 2019. "A Revision on Geodesic Pseudo-Convex Combination and Knaster–Kuratowski–Mazurkiewicz Theorem on Hadamard Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1186-1198, September.

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