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September 10, 2025Open Access

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

Key Points

New inequalities broaden the understanding of (h,m)-convexity and enhance existing literature.
The use of classical inequalities like Hölder and Young establishes a refined analytical approach.
The findings may enable flexibility in mathematical analysis and provide insights into applied settings.
Incorporation of weighted integrals allows for a more comprehensive exploration of convex functions.

Abstract

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.

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