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

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