log-convex function

‎We obtain some new Jensen-Mercer type inequalities for log-convex functions‎. ‎Indeed‎, ‎we establish refinement and reverse for the Jensen-Mercer inequality for log-convex functions‎. ‎Several new Hermite-Hadamard and Fej\'er types of inequalities are also presented‎.‎

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.