On geodesic convex and generalized geodesic convex functions over Riemannian manifolds

Abstract

In this paper, we have obtained geodesic convex and geodesic pseudoconvex functions from the ratio of the square of a non-negative geodesic convex to a strictly positive geodesic concave; and by the ratio of a geodesic convex and related functions to a positive affine and some generalized convex functions, respectively, over Riemannian manifolds. Further, we have proved that the ratio of a non-negative geodesic convex to a positive geodesic concave function is a geodesic quasiconvex function.