The Best Constant For Inequality Involving Sum Of The Reciprocals And Product Of Positive Numbers With Unit Sum
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914715227127808 |
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| author | Aliyev, Yagub N. |
| author_facet | Aliyev, Yagub N. |
| contents | In the paper we study a special parameter containing algebraic inequality involving sum of reciprocals and product of positive real numbers whose sum is 1. We determine the best values of the parameter using a new optimization argument. In the case of three numbers the algebraic inequality have some interesting geometric applications involving a generalization of Euler's inequality about the ratio of radii of circumscribed and inscribed circles of a triangle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17481 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Best Constant For Inequality Involving Sum Of The Reciprocals And Product Of Positive Numbers With Unit Sum Aliyev, Yagub N. Classical Analysis and ODEs 26D05, 52A40 In the paper we study a special parameter containing algebraic inequality involving sum of reciprocals and product of positive real numbers whose sum is 1. We determine the best values of the parameter using a new optimization argument. In the case of three numbers the algebraic inequality have some interesting geometric applications involving a generalization of Euler's inequality about the ratio of radii of circumscribed and inscribed circles of a triangle. |
| title | The Best Constant For Inequality Involving Sum Of The Reciprocals And Product Of Positive Numbers With Unit Sum |
| topic | Classical Analysis and ODEs 26D05, 52A40 |
| url | https://arxiv.org/abs/2311.17481 |