# 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 *h*-preinvexity, we present weighted
integral inequalities of Hermite–Hadamard-type for functions whose derivatives
in absolute value raised to certain powers are *h*-preinvex functions. Some
new Hermite–Hadamard-type integral inequalities are obtained when *h* is
super-additive. Inequalities of Hermite–Hadamard-type for *s*-preinvex
functions are given as well as a special case of our results.

# Acknowledgements

The authors thank the anonymous referee for his/her very useful comments which helped us to improve the final version of the manuscript.

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**Received:**2014-09-26

**Accepted:**2014-11-13

**Published Online:**2017-01-19

**Published in Print:**2018-09-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston