Generalized geodesic convexity on Riemannian manifolds

Izhar Ahmad, Meraj Ali Khan*, Amira A. Ishan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Article number547
Issue number6
StatePublished - 2019

Bibliographical note

Funding 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

Publisher Copyright:
© 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)


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