New Generalization of Geodesic Convex Function

Abstract

As a generalization of a geodesic function, this paper introduces the notion of the geodesic φE-convex function. Some properties of the φE-convex function and geodesic φE-convex function are established. The concepts of a geodesic φE-convex set and φE-epigraph are also given. The characterization of geodesic φE-convex functions in terms of their φE-epigraphs, are also obtained.

Keywords

• Riemannian manifolds
• geodesic
• <i>E</i>-convex sets
• <i>φ_E</i>-convex function
• geodesic <i>φ_E</i>-convex function