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.
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