Generalized Geodesic Convexity on Riemannian Manifolds

Izhar Ahmad, Meraj Ali Khan and Amira A. Ishan
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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

Mathematics, 2019, vol. 7, issue 6, 1-12

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.

Keywords: geodesic log-invex function; geodesic log-preinvex function; global minimum; mean value inequality; Riemannian manifolds (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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