Hermite–Hadamard-type inequalities for geometrically r-convex functions in terms of Stolarsky’s mean with applications to means

Abstract

Abstract In this paper, we obtain new Hermite–Hadamard-type inequalities for r-convex and geometrically convex functions and, additionally, some new Hermite–Hadamard-type inequalities by using the Hölder–İşcan integral inequality and an improved power-mean inequality.

Keywords

• Hermite–Hadamard’s inequality
• Stolarsky’s mean
• Convex function
• r-convex function
• Hölder’s inequality
• Hölder–İşcan inequality