A new concept generalized (h,m)−preinvex function on Yang’s fractal sets is proposed. Some Ostrowski’s type inequalities with two parameters for generalized (h,m)−preinvex function are established, where three local fractional inequalities involving generalized midpoint type, trapezoid type and Simpson type are derived as consequences. Furthermore, as some applications, special means inequalities and numerical quadratures for local fractional integrals are discussed.

A new concept generalized (h,m)−preinvex function on Yang’s fractal sets is proposed. Some Ostrowski’s type inequalities with two parameters for generalized (h,m)−preinvex function are established, where three local fractional inequalities involving generalized midpoint type, trapezoid type and Simpson type are derived as consequences. Furthermore, as some applications, special means inequalities and numerical quadratures for local fractional integrals are discussed.