Multi-parametric post quantum Simpson inequalities and their applications

In this paper, the authors established some very general analogues of Simpson type inequalities via newly defined two types of quantum integrals over a finite interval. Firstly, a multi-parameters identity is developed. Applying this generic identity as an auxiliary result, we derive several Simpson type quantum inequalities for those functions whose absolute value of first-order quantum derivatives are m-convex. The results of this study generate a family of interesting special cases. Finally, in order to show the efficiency of our results, several applications are obtained about the special means of different positive real numbers.