Copyright © 2009 I. Ahmad et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The present paper deals with the properties of geodesic -preinvex functions and their relationships with -invex functions and strictly geodesic -preinvex functions. The geodesic -pre-pseudo-invex and geodesic -pre-quasi-invex functions on the geodesic invex set are introduced and some of their properties are discussed.