Inequalities on a Class of Function Sets
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916038145212416 |
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| author | Leng, Gangsong |
| author_facet | Leng, Gangsong |
| contents | We prove a functional extension of an exponential inequality originally proposed by Bin Zhao and proved by Xiaosheng Mou. The main result asserts that if $α_1\leq \cdots\leq α_n$ and $\sum_{k=1}^n α_k=0$, then \[ \sum_{k=1}^n ϕ(kα_k)\geq 0 \] for every odd function $ϕ$ that is increasing and convex on $[0,\infty)$. The proof is based on a truncated-sum comparison and the stop-loss characterization of the increasing convex order. As consequences, we recover the original exponential inequality and obtain polynomial and integral variants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23143 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inequalities on a Class of Function Sets Leng, Gangsong Functional Analysis 26D15, 26A51, 60E15 We prove a functional extension of an exponential inequality originally proposed by Bin Zhao and proved by Xiaosheng Mou. The main result asserts that if $α_1\leq \cdots\leq α_n$ and $\sum_{k=1}^n α_k=0$, then \[ \sum_{k=1}^n ϕ(kα_k)\geq 0 \] for every odd function $ϕ$ that is increasing and convex on $[0,\infty)$. The proof is based on a truncated-sum comparison and the stop-loss characterization of the increasing convex order. As consequences, we recover the original exponential inequality and obtain polynomial and integral variants. |
| title | Inequalities on a Class of Function Sets |
| topic | Functional Analysis 26D15, 26A51, 60E15 |
| url | https://arxiv.org/abs/2605.23143 |