In this article, we use quantum integrals to derive Hermite–Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We the q?2-quantum integral show midpoint trapezoidal q?2-differentiable functions. Furthermore, an example that previously proved Hermite–Hadamard-type inequality via q?1-quantum is not valid functions, present its proper form. q?1-...

Abstract In this paper, we establish some new $(p,q)$ ( p , q ) -integral inequalities of Simpson’s second type for preinvex functions. Many results given in paper provide generalizations and extensions the previous research. Moreover, exampl...