On some inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula

摘要

Some inequalities are presented here for differentiable convex mappings, using Hermite–Hadamard's integral inequality holding for convex functions. A parallel development is deduced for differentiable concave functions. Some applications to special means of real numbers are also given. Finally, some error estimates for the midpoint formula are obtained.