In this paper, we establish some new inequalities of Hermite-Hadamard type based on preinvexity for differentiable mapping that are linked with the illustrious Hermite-Hadamard type inequality for mappings whose derivatives are preinvexity. Also a parallel development is made base on concavity. Applications to some special means of real numbers are found. Also applications to numerical integration are provided. This contributes to new better estimates than presented already
