On new trapezoid and midpoint type inequalities for generalized quantum integrals

In this article, by utilizing the functions with bounded second derivatives, we first prove some trapezoid and midpoint type inequalities for generalized quantum integrals which are introduced in the recent papers. Then we establish some new quantum integral inequalities for mappings whose second quantum derivatives are bounded. Moreover, we obtain some new weighted trapezoid and midpoint type inequalities for generalized quantum integrals by using the functions with bounded second derivatives. Finally, we investigate the connections between our results and those in earlier works.