Hermite–Hadamard Framework for \((h,m)\)-Convexity

This work presents a generalization and extension of previous results by incorporating weighted integrals and a refined class of second-type \((h,m)\)-convex functions. By utilizing classical inequalities, such as those of Hölder, Young and the Power mean, we establish new Hermite-Hadamard-type inequalities. The findings offer a broader and more flexible analytical framework, enhancing existing results in the literature. Potential applications of the developed inequalities are also explored.