Unifying inequalities of Hardy, Copson, and others
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| 024 | 7 | 0 | |a 10.1007/s00010-013-0230-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-013-0230-x | ||
| 245 | 0 | 0 | |a Unifying inequalities of Hardy, Copson, and others |h [Elektronische Daten] |c [H. Carley, P. Johnson Jr., R. Mohapatra] |
| 520 | 3 | |a In order to provide an alternative proof to an inequality of Hilbert, Hardy proved $$\sum_{n=0}^{\infty} \left((n+1)^{-1} \sum_{k=0}^{n}x_k\right)^p \leq\left(\frac{p}{p-1} \right)^p\sum_{n=0}^\infty x_n^p. $$ ∑ n = 0 ∞ ( n + 1 ) - 1 ∑ k = 0 n x k p ≤ p p - 1 p ∑ n = 0 ∞ x n p . This inequality and its relatives triggered research activity concerning norm inequalities including new inequalities by Copson and Levinson. In this paper, three theorems are established from which related inequalities of Hardy, Copson, and Levinson and various extensions are deduced as corollaries. | |
| 540 | |a Springer Basel, 2013 | ||
| 700 | 1 | |a Carley |D H. |u Department of Mathematics, New York City College of Technology-CUNY, 11201, Brooklyn, NY, USA |4 aut | |
| 700 | 1 | |a Johnson Jr. |D P. |u Department of Math and Statistics, Auburn University, 36849, Auburn, AL, USA |4 aut | |
| 700 | 1 | |a Mohapatra |D R. |u Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA |4 aut | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 497-510 |x 0001-9054 |q 89:3<497 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-013-0230-x |q text/html |z Onlinezugriff via DOI |
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| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
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| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-013-0230-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Carley |D H. |u Department of Mathematics, New York City College of Technology-CUNY, 11201, Brooklyn, NY, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Johnson Jr |D P. |u Department of Math and Statistics, Auburn University, 36849, Auburn, AL, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Mohapatra |D R. |u Department of Mathematics, University of Central Florida, 32816, Orlando, FL, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/3(2015-06-01), 497-510 |x 0001-9054 |q 89:3<497 |1 2015 |2 89 |o 10 | ||