Abstract
In this paper, by using a weighted identity for functions defined on an open
invex subset of the set of real numbers, by using the Hölder integral
inequality and by using the notion of
-preinvexity, we present weighted
integral inequalities of Hermite–Hadamard-type for functions whose derivatives
in absolute value raised to certain powers are
-preinvex functions. Some
new Hermite–Hadamard-type integral inequalities are obtained when
is
super-additive. Inequalities of Hermite–Hadamard-type for
-preinvex
functions are given as well as a special case of our results.