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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| _version_ | 1832562313428729856 |
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| author | Aleksandra Čižmešija Sabir Hussain Josip Pečarić |
| author_facet | Aleksandra Čižmešija Sabir Hussain Josip Pečarić |
| author_sort | Aleksandra Čižmešija |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-379defc36b7f4f9c8171fb3d2c3679e3 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-379defc36b7f4f9c8171fb3d2c3679e32025-02-03T01:22:54ZengWileyJournal of Function Spaces and Applications0972-68022009-01-017216718610.1155/2009/695685Some new refinements of strengthened Hardy and Pólya–Knopp's inequalitiesAleksandra Čižmešija0Sabir Hussain1Josip Pečarić2Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, CroatiaAbdus Salam School of Mathematical Sciences, GC University, 35-C-II, M. M. Alam Road, Gulberg III, Lahore-54660, PakistanFaculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10000 Zagreb, CroatiaWe 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.http://dx.doi.org/10.1155/2009/695685 |
| spellingShingle | Aleksandra Čižmešija Sabir Hussain Josip Pečarić Some new refinements of strengthened Hardy and Pólya–Knopp's inequalities Journal of Function Spaces and Applications |
| title | Some new refinements of strengthened Hardy and Pólya–Knopp's inequalities |
| title_full | Some new refinements of strengthened Hardy and Pólya–Knopp's inequalities |
| title_fullStr | Some new refinements of strengthened Hardy and Pólya–Knopp's inequalities |
| title_full_unstemmed | Some new refinements of strengthened Hardy and Pólya–Knopp's inequalities |
| title_short | Some new refinements of strengthened Hardy and Pólya–Knopp's inequalities |
| title_sort | some new refinements of strengthened hardy and polya knopp s inequalities |
| url | http://dx.doi.org/10.1155/2009/695685 |
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