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.
Bibliographical noteFunding Information:
We thank three anonymous referees very much for many valuable remarks and suggestions that definitely improved the final version of the paper. This research was funded by the Deanship of Scientific Research, University of Tabuk, KSA
© 2019 by the authors.
- Geodesic log-invex function
- Geodesic log-preinvex function
- Global minimum
- Mean value inequality
- Riemannian manifolds
ASJC Scopus subject areas
- Mathematics (all)