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