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.