Trapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculus

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-differentiable It also demonstrated by considering limit q?1? ??2,?1=???1,?2=?2??1 in newly derived results, findings can be turned into certain known results.