New Inequalities of Hermite-Hadamard Type for n-Times Differentiable Convex and Concave Functions with Applications

Abstract

In this paper, a new identity for n-times differntiable functions is established and by using the obtained identity, some new inequalities Hermite-Hadamard type are obtained for functions whose nth derivatives in absolute value are convex and concave functions. From our results, several inequalities
of Hermite-Hadamard type can be derived in terms of functions whose frst and second derivatives in absolute value are convex and concave functions as special cases. Our results may provide renements of some results already exist in literature. Applications to trapezoidal formula and special means of
established results are given.