On General Local Fractional Integral Inequalities for Generalized H-Preinvex Functions on Yang’s Fractal Sets

In this paper, based on Yang’s fractal theory, the Hermite–Hadamard’s inequalities for generalized [Formula: see text]-preinvex function are proved. Then, using the local fractional integral identity proposed by Sun [Some local fractional integral inequalities for generalized preinvex functions and applications to numerical quadrature, Fractals 27(5) (2019) 1950071] as auxiliary function, some parameterized local fractional integral inequalities for generalized [Formula: see text]-preinvex functions are established. For the special cases of the parameters, some generalized Simpson-type, midpoint-type and trapezoidal inequalities are established. Finally, some applications of these inequalities in numerical integration are proposed.