摘要：In this research, we derive two generalized integral identities involving the $q^{ arkappa _{2}}$ -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 for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson’s and Newton’s type inequalities by considering the limit $q ightarrow 1^{-}$ in the key results of this paper.
关键词：Simpson’s ( rac{1}{3}) formula ; Simpson’s ( rac{3}{8}) formula ; Integral inequalities ; Quantum calculus ; Preinvex functions
