Some results on $\varphi$--convex functions and geodesic $\varphi$-convex functions

Abstract

As a generalization of geodesic function, in the present paper, we introduce the notion of geodesic $\varphi$-convex function and deduce some basic properties of $\varphi$-convex function and geodesic $\varphi$-convex function. We also introduce the concept of geodesic $\varphi$-convex set and $\varphi$-epigraph and investigate a characterization of geodesic $\varphi$-convex functions in terms of their $\varphi$-epigraphs.