Some new refinements of strengthened Hardy and Pólya–Knopp′s inequalities

Abstract

Abstract. We prove a new general one-dimensional inequality for convex functions and Hardy-Littlewood averages. Furthermore, we apply this result to unify and refine the so-called Boas's inequality and the strengthened inequalities of the Hardy-Knopp-type, deriving their new refinements as special cases of the obtained general relation. In particular, we get new refinements of strengthened versions of the well-known Hardy and Pólya-Knopp's inequalities.