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

Abstract

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

arXiv comment14 pages

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