Some new refinement of Hermite-Hadamard type inequalities and their applications

Abstract

In this paper first, we prove some new refinement of Hermite-Hadamard type inequalities for the convex function $f$. Second, by using five new integral identities, we present some new Riemann-Liouville fractional trapezoid and midpoint type inequalities. Third, using these results, we present applications to $f$-divergence measures. At the end, some new bounds for special means of different positive real numbers and new error estimates for the trapezoidal and midpoint formula are provided as well. These results give us the generalizations and improvements of the earlier results.