On new trapezoid and midpoint type inequalities for generalized quantum integrals

Abstract

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