Variants of the Damascus inequality
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914403874504704 |
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| author | Sujsuntinukul, Chanatip Chesneau, Christophe |
| author_facet | Sujsuntinukul, Chanatip Chesneau, Christophe |
| contents | In 2016, Dannan and Sitnik established the notable Damascus inequality, which features a symmetric structure under a multiplicative constraint. In this study, we consider the natural generalisation of this inequality by characterising all positive integers $m$ and $n$ such that the inequality \[\sum_{j=1}^m\frac{x_j^n-1}{x_{j}^{n+1}+1}\leqslant 0\] holds for any positive real numbers $x_1, \ldots, x_m$ with $\prod_{j=1}^mx_j=1$. Our approach relies on the theories of GA-convexity and Sturm's sequence. For the cases where the inequality fails, we also investigate the topological properties of the set of non-solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00916 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variants of the Damascus inequality Sujsuntinukul, Chanatip Chesneau, Christophe General Mathematics 26D15 In 2016, Dannan and Sitnik established the notable Damascus inequality, which features a symmetric structure under a multiplicative constraint. In this study, we consider the natural generalisation of this inequality by characterising all positive integers $m$ and $n$ such that the inequality \[\sum_{j=1}^m\frac{x_j^n-1}{x_{j}^{n+1}+1}\leqslant 0\] holds for any positive real numbers $x_1, \ldots, x_m$ with $\prod_{j=1}^mx_j=1$. Our approach relies on the theories of GA-convexity and Sturm's sequence. For the cases where the inequality fails, we also investigate the topological properties of the set of non-solutions. |
| title | Variants of the Damascus inequality |
| topic | General Mathematics 26D15 |
| url | https://arxiv.org/abs/2601.00916 |