On Hermite–Hadamard–Fejér Inequalities Within Postquantum Coordinate Frameworks

Source abstract

In this paper, we investigate new forms of Hermite–Hadamard–Fejér type inequalities on the coordinates within the framework of postquantum (p,q)‐calculus. By extending the classical Hermite–Hadamard–Fejér inequalities to the setting of coordinated convex functions, we establish several novel integral inequalities involving (p,q)‐derivatives and (p,q)‐integrals. The results presented here provide a unified approach that not only generalizes existing inequalities in quantum and classical calculus but also yields sharp estimations in the postquantum context. Potential applications of these results are discussed, highlighting their significance in the broader theory of inequalities and in the development of analytical tools for applied mathematics.