Characterizations of geodesic sub-b-s-convex functions on Riemannian manifolds

In this paper, we present the notion of geodesic sub- b - s -convex function on the Riemannian manifolds. A non-trivial example of geodesic sub- b - s -convex function but not geodesic convex function is also discussed. Some fundamental properties of geodesic sub- b - s -convex functions are investigated. Moreover, we derive the optimality conditions of unconstrained and constrained programming problems under the sub- b - s -convexity.