New Weighted Inequalities for Higher Order Derivatives and Applications

Abstract

We establish a new Ostrowski type inequality for (n + 1)-times differentiable mappings which are bounded. Then, some new inequalities of Hermite-Hadamard type are obtained for functions whose (n + 1) th derivatives in absolute value are convex. Spacial cases of these inequalities reduce some well known inequalities. With the help of obtained inequalities, we give applications for the kth-moment of random variables.