engleski

Some new refinements of Hardy and P\'{;o};lya-Knopp's inequalities

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 P\'{;o};lya--Knopp's inequalities.

Integral inequalities; Boas's inequality; Hardy--Littlewood average; Hardy's inequality;

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