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Generalized Geodesic Convexity on Riemannian Manifolds

Author

Listed:
  • Izhar Ahmad

    (Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Meraj Ali Khan

    (Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Amira A. Ishan

    (Department of Mathematics, Taif University, Taif 21944, Saudi Arabia)

Abstract

We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic log-preinvexity is extended to Cartan-Hadamard manifolds.

Suggested Citation

  • Izhar Ahmad & Meraj Ali Khan & Amira A. Ishan, 2019. "Generalized Geodesic Convexity on Riemannian Manifolds," Mathematics, MDPI, vol. 7(6), pages 1-12, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:547-:d:240307
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    References listed on IDEAS

    as
    1. Akhlad Iqbal & Shahid Ali & I. Ahmad, 2012. "On Geodesic E-Convex Sets, Geodesic E-Convex Functions and E-Epigraphs," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 239-251, October.
    2. I. Ahmad & Akhlad Iqbal & Shahid Ali, 2009. "On Properties of Geodesic 𠜂 -Preinvex Functions," Advances in Operations Research, Hindawi, vol. 2009, pages 1-10, April.
    Full references (including those not matched with items on IDEAS)

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