quasiconvex functions

In this paper relation between pseudoconvex and quasi convex functions is introduced in the context of Riemannian manifolds. In this setting first order characterization of pseudoconvex (strongly pseudoconvex) functions is obtained.

In this paper, we give some inequalities for dierentiable convex functions which are connected with the Hermite-Hadamard's integral inequality holding for convex functions. Also, we obtain some estimates to the right-hand side of Hermite-Hadamard inequality for functions whose absolute values of fourth derivatives raised to positive real powers are m-convex. Finally, some natural applications to special means of real numbers are given.