Some new refinements of strengthened Hardy and Pólya–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...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/695685 |
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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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| ISSN: | 0972-6802 |