Hermite-Hadamard-Type Inequalities for h -Preinvex Functions via Generalized Fractional Integrals

Abstract

Research on fractional-order Hermite-Hadamard (H-H) inequalities has predominantly relied on single convexity assumptions, limiting its adaptability to generalized convexity contexts such as h-preinvex functions. This paper refines the framework of fractional-order H-H inequalities for preinvex functions by leveraging the generalized Riemann-Liouville fractional integral operator. Specifically, a novel class of H-H-type inequalities is constructed and rigorously proved for h-preinvex functions. These results not only generalize and improve classical findings in existing literature but also reveal intrinsic connections between the inequalities. The validity of our conclusions is demonstrated through concrete examples and numerical visualizations, offering new insights for generalized convexity theory and fractional integral inequalities.