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

Abstract

In this research, we derive two generalized integral identities involving the 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 for q-differentiable preinvex functions. Moreover, we obtain some new and known Simpson’s and Newton’s type inequalities by considering the limit q→ 1 − in the key results of this paper.