Improved Maclaurin type inequalities involving local fractional integrals for generalized s -preinvex functions and numerical integration

In this work, we first establish a three-point local fractional Maclaurin-type identity under Yang's fractal system. Using the generalized Holder inequality and its improved version, we derive two Maclaurin type inequalities through local fractional integrals for generalized s-preinvex functions, from which several corollaries are obtained as special cases. To verify the theoretical results and compare the accuracy of error bounds derived from the two approaches, we present two numerical examples with 2D and 3D simulation illustrations. Finally, we apply these inequalities to construct error estimates for local fractional Maclaurin-type numerical integration formulas, demonstrating their practical utility.