Some new refinements of strengthened Hardy and Pólya-Knopp's inequalities. (Q841318)
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scientific article; zbMATH DE number 5604136
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some new refinements of strengthened Hardy and Pólya-Knopp's inequalities. |
scientific article; zbMATH DE number 5604136 |
Statements
Some new refinements of strengthened Hardy and Pólya-Knopp's inequalities. (English)
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15 September 2009
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Summary: 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.
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integral inequalities
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Boas's inequality
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Hardy-Littlewood average
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Hardy's inequality
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Pólya-Knopp's inequality
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weights
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power weights
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convex functions
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0.9715726
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0.9144939
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0.9133624
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0.91085356
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