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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2022
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2209.05560 |
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| _version_ | 1866910544968024064 |
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| author | Mukherjee, Himadri |
| author_facet | Mukherjee, Himadri |
| contents | Aim of this article is to prove the inequality $n \sum_{i=1}^{n} a_ib_i \leq \sum_{i=1}^{n} a_i \sum_{i=1}^n b_i$ when $a_i$ are $n$ increasing positive real numbers and $b_i$ are $n$ decreasing real numbers. We also prove generalizations of this result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_05560 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | An inequality generalizing $AM \geq GM$ and $AM \geq HM$ Mukherjee, Himadri Combinatorics Classical Analysis and ODEs Number Theory 39B05 Aim of this article is to prove the inequality $n \sum_{i=1}^{n} a_ib_i \leq \sum_{i=1}^{n} a_i \sum_{i=1}^n b_i$ when $a_i$ are $n$ increasing positive real numbers and $b_i$ are $n$ decreasing real numbers. We also prove generalizations of this result. |
| title | An inequality generalizing $AM \geq GM$ and $AM \geq HM$ |
| topic | Combinatorics Classical Analysis and ODEs Number Theory 39B05 |
| url | https://arxiv.org/abs/2209.05560 |