SOME NEW INEQUALITIES ON GENERALIZATION OF HERMITE-HADAMARD AND BULLEN TYPE INEQUALITIES, APPLICATIONS TO TRAPEZOIDAL AND MIDPOINT FORMULA

Abstract

In this paper, we give a new general identity for differentiable functions. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Bullen type for functions whose derivatives in absolute value at certain power are convex. Some applications to special means of real numbers are also given. Finally, some error estimates for the trapezoidal and midpoint formula are addressed.