On Hermite--Hadamard Type Integral Inequalities for $n$-times Differentiable $m$- and ($\alpha,m$)-Logarithmically Convex Functions

M. A. Latif, S. S. Dragomir, E. Momoniat

In this paper, we establish Hermite--Hadamard type inequalities for functions whose $n$th derivatives are $m$- and $(\alpha,m)$-logarithmically convex functions. From our results, several results for classical trapezoidal and classical midpoint inequalities are obtained in terms second derivatives that are $m$- and $(\alpha,m)$-logarithmically convex functions as special cases.