LAUSR

We investigate the class of H-invex functions including, e.g., the subclasses of convex, c-strongly convex, $$ \varphi $$φ-uniformly convex and superquadratic functions. For H-invex functions we prove Fejér and Hermite–Hadamard type inequalities. We generalize some results by Abramovich et al. (J Math Anal Appl 344:1048–1556, 2008), Banić et al. (J Korean Math Soc 45:513–525, 2008), and Merentes et al. (Aequ Math 80:193–199, 2010).