Some Hermite–Hadamard-mercer Inequalities on the Coordinates on Post Quantum

Abstract In this paper, we develop new Hermite-Hadamard-Mercer type inequalities on coordinates via post-quantum calculus, also known as (p, q) - calculus. By introducing novel (p1, p2, q1, q2)-differentiable and (p1, p2, q1, q2)-integrable functions, we generalize classical results and extend previous inequalities under the setting of coordinate convexity. Several new identities are derived, which naturally reduce to known results when specific parameters are chosen. Numerical examples and visualizations are also provided to illustrate the utility of our results.