Some Hermite–Hadamard type inequalities for generalized h-preinvex function via local fractional integrals and their applications

The concept of generalized h-preinvex function on real linear fractal sets Rβ R β ( 0 < β ≤ 1 0 < β ≤ 1 ) is introduced, which extends generalized preinvex, generalized s-preinvex, generalized Godunova–Levin preinvex, and generalized P-preinvex functions. In addition, some Hermite–Hadamard type inequalities for these classes of functions involving local fractional integrals are established. Lastly, the upper bounds for generalized expectation, generalized rth moment, and generalized variance of a continuous random variable are given to illustrate the applications of the obtained results.