On Geodesic E‐Convex Sets, Geodesic E‐Convex Functions and E‐Epigraphs

In this paper, we introduce a new class of sets and a new class of functions called geodesic E‐convex sets and geodesic E‐convex functions on a Riemannian manifold. The concept of E‐quasiconvex functions on R ⁿ is extended to geodesic E‐quasiconvex functions on Riemannian manifold and some of its properties are investigated. Afterwards, we generalize the notion of epigraph called E‐epigraph and discuss a characterization of geodesic E‐convex functions in terms of its E‐epigraph. Some properties of geodesic E‐convex sets are also studied.