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We prove a new general one-dimensional inequality for convexfunctions and Hardy–Littlewood averages. Furthermore, we apply this result tounify and refine the so-called Boas's inequality and the strengthened inequalitiesof the Hardy–Knopp–type, deriving their new refinements as special cases of theobtained general relation. In particular, we get new refinements of strengthenedversions of the well-known Hardy and Pólya–Knopp's inequalities

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