The inequality of Milne and its converse
<p/> <p>We prove: Let <inline-formula><graphic file="1029-242X-2002-241023-i1.gif"/></inline-formula> be real numbers with <inline-formula><graphic file="1029-242X-2002-241023-i2.gif"/></inline-formula>. Then we have for all real nu...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2002-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/7/241023 |
| Summary: | <p/> <p>We prove: Let <inline-formula><graphic file="1029-242X-2002-241023-i1.gif"/></inline-formula> be real numbers with <inline-formula><graphic file="1029-242X-2002-241023-i2.gif"/></inline-formula>. Then we have for all real numbers <inline-formula><graphic file="1029-242X-2002-241023-i3.gif"/></inline-formula>: <inline-formula><graphic file="1029-242X-2002-241023-i4.gif"/></inline-formula> with the best possible exponents <inline-formula><graphic file="1029-242X-2002-241023-i5.gif"/></inline-formula> and <inline-formula><graphic file="1029-242X-2002-241023-i6.gif"/></inline-formula>. The left-hand side of (0.1) with <inline-formula><graphic file="1029-242X-2002-241023-i7.gif"/></inline-formula> is a discrete version of an integral inequality due to E.A. Milne [1]. Moreover, we present a matrix analogue of (0.1).</p> |
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| ISSN: | 1025-5834 1029-242X |