Quantum Hermite-Hadamard type inequalities for generalized strongly preinvex functions

In accordance with the quantum calculus, the quantum Hermite-Hadamard type inequalities shown in recent findings provide improvements to quantum Hermite-Hadamard type inequalities. We acquire a new q(kappa 1)-integral and q(kappa 2)-integral identities, then employing these identities, we establish new quantum Hermite-Hadamard q(kappa 1)-integral and q(kappa 2)-integral type inequalities through generalized higher-order strongly preinvex and quasi-preinvex functions. The claim of our study has been graphically supported, and some special cases are provided as well. Finally, we present a comprehensive application of the newly obtained key results. Our outcomes from these new generalizations can be applied to evaluate several mathematical problems relating to applications in the real world. These new results are significant for improving integrated symmetrical function approximations or functions of some symmetry degree.