Properties and integral inequalities of Hadamard- Simpson type for the generalized ( s , m ) -preinvex functions

The authors introduce the concepts of m-invex set, generalized ( s , m ) -preinvex function, and explicitly ( s , m ) -preinvex function, provide some properties for the newly introduced functions, and establish new Hadamard-Simpson type integral inequalities for a function of which the power of the absolute of the first derivative is generalized ( s , m ) -preinvex function. By taking different values of the parameters, Hadamardtype and Simpson-type integral inequalities can be deduced. Furthermore, inequalities obtained in special case present a refinement and improvement of previously known results.