Strong geodesic α-preinvexity and invariant α-monotonicity on riemannian manifolds

摘要

In this article, we introduce and study a new class of generalized convex functions on Riemannian manifold, called strongly -invex and strongly geodesic -preinvex functions. Several kinds of invariant -monotonicities on Riemannian manifold are introduced. We establish the relationships among the strong -invexity, strong geodesic -preinvexity and invariant -monotonicities under suitable conditions. Various types of -invexities for functions on Riemannian manifolds are introduced and relations among them are established.