New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

Abstract

Abstract In this research, we derive two generalized integral identities involving the $q^{\varkappa _{2}}$ qϰ2 -quantum integrals and quantum numbers, the results are then used to establish some new quantum boundaries for quantum Simpson’s and quantum Newton’s inequalities forq-differentiable preinvex functions. Moreover, we obtain some new and known Simpson’s and Newton’s type inequalities by considering the limit $q\rightarrow 1^{-}$ q→1− in the key results of this paper.