| 摘要: |
| 对数凹函数Lp混合积分的Lp混合Shephard问题问: 对于$p\geq1$, $y\in\R^{n}$, 若$h\left(\intl f,y)\le h(\intl g,y\right)$, 能否推出当$p
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| 关键词: Lp 混合Shephard问题 对数凹函数 Lp混合投影体 Lp混合积分 |
| DOI： |
| 分类号:O186.5 |
| 基金项目:国家自然科学基金面上项目 (12471055) |
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| The Lp-mixed Shephard problem on the Lp-mixed integral of log-concave functions |
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LI Shuxian, MA Dan
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Shanghai Normal University
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| Abstract: |
| The Lp-mixed Shephard problem on Lp-mixed integral of log-concave functions asks: For $p\geq1$, $y\in\R^{n}$, whether $h\left(\intl f,y)\le h(\intl g,y\right)$ implies $V_{p,i}(f,h)\le V_{p,i}(g,h)$ for $p < n-i$, $V_{p,i}(f,h)\ge V_{p,i}(g,h)$ for $0 < n-i< p$? Here, $\intl f$ is the Lp-mixed projection body of a log-concave function f, $V_{p,i}$ is the Lp-mixed integral of log-concave functions. Special cases are solved in this paper. |
| Key words: The Lp-mixed Shephard problem log-concave function Lp-mixed projection body Lp-mixed integral |
