The objective of this paper is to obtain some Hermite-Hadamard type inequalities for h-preinvex functions. Firstly, a new kind of generalized h-convex functions, termed h-preinvex functions, is introduced through relaxing the concept of h-convexity introduced by Varosanec. Some Hermite-Hadamard type inequalities for h-preinvex functions are established under certain conditions. Our results can be viewed as generalization of several previously known results. Results proved in this paper may stimulate further research in different areas of pure and applied sciences.

The main objective of this article is to establish some new fractional refinements of Hermite–Hadamard-type inequalities essentially using newψk-Riemann–Liouville fractional integrals, wherek>0. Using this new fractional integral, we also derive two new fractional integral identities. Applications of the obtained results are also discussed.