HERMITE–HADAMARD TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED s-PREINVEX FUNCTIONS AND THEIR GENERALIZATION

In this paper, the definition of generalized s-preinvex function on Yang’s fractal sets [Formula: see text] is proposed, and the generalized Hermite–Hadamard’s inequality for this class of functions is established. By using this convexity, some generalized Hermite–Hadamard type integral inequalities with parameters are established. For these inequalities, the absolute values of twice local fractional order derivative of the functions are generalized s-preinvex functions. Some special integral inequalities can be obtained by assigning special values to the obtained inequalities, and two examples are given to illustrate our results. Finally, we propose the applications of the results in numerical integration and error estimation.