On Generalized Hermite–Hadamard-Type Inequalities for Convexity with Computational Analysis and Their Applications

This paper establishes a new general integral identity for differentiable functions involving weighted fractional integral operators. By applying this identity together with s-convexity and s-uniform convexity with modulo Φ, we derive several refined Hermite–Hadamard inequalities. Our results generalize and unify multiple classical and recent inequalities reported in the literature, which are recovered as special cases under a specific weighting selection. Furthermore, we demonstrate the applicability of the established bounds through concrete evaluations involving special means of real numbers, the q-digama function, and the modified Bessel function. Finally, our theoretical bounds are validated using 2D/3D visual representations and numerical simulations.