Properties of GA-h-Convex Functions in Connection to the Hermite–Hadamard–Fejér-Type Inequalities

In this study, the Hermite–Hadamard–Fejér inequalities for $GA$-h-convex are proved, and the results for particular classes of functions are highlighted. In addition, several generalizations of the Hermite–Hadamard inequalities are presented. Some features of functions $\mathcal{H}$ and $\mathcal{F}$ that are naturally linked to the Hermite–Hadamard–Fejér-type inequalities for $GA$-h-convex have also been discussed. Finally, we obtain applications of the results related to the p-logarithmic mean and the mean of order p.