Some Hermite-Hadamard type inequalities for GA-s-convex functions in the fourth sense

In the present manuscript, we define the concept of GA-s-convex functions in the fourth sense. We obtain the Hermite-Hadamard inequality for the newly introduced class of functions. We also establish some inequalities of the Hermite-Hadamard type for functions whose first derivative in absolute value at certain powers is a GA-s-convex function in the fourth sense. In the last, some applications to special means of real numbers are given.

Automated summary

In this manuscript, we introduce the concept of GA-s-convex functions in the fourth sense and derive the Hermite-Hadamard inequality for this newly introduced class of functions. We also establish some Hermite-Hadamard type inequalities for functions whose absolute value of the first derivative at certain powers is a GA-s-convex function in the fourth sense. Finally, we provide some applications to special means of real numbers.