| 球面空间中的Pedoe不等式与张-杨不等式及应用 |
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| 引用本文： | 杨世国,齐继兵,王文.球面空间中的Pedoe不等式与张-杨不等式及应用[J].数学杂志,2014,34(1):123-129. |
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| 作者姓名： | 杨世国 齐继兵 王文 |
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| 作者单位： | 合肥师范学院数学系和教师教育研究中心;安徽新华学院 |
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| 基金项目： | 国家自然科学基金(60671051)资助项目;高等学校博士学科点专项科研基金项目(20113401110009);安徽省高等学校自然科学基金项目(KJ2011B133) |
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| 摘 要： | 本文应用距离几何的理论与方法,研究了n维球面空间中n维单形与有限点集的几何不等式问题,建立了球面空间中n维单形一种形式的Pedoe不等式与有限点集一种形式的张-杨不等式,并应用它获得n维球面空间中Veljan-Korchmaros型不等式与Finsler-Hadwinger型不等式.
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| 关 键 词： | 球面空间 单形 有限点集 几何不等式 |
| 收稿时间： | 2011/12/2 0:00:00 |
| 修稿时间： | 2012/4/11 0:00:00 |
THE PEDOE INEQUALITY AND ZHANG-YANG INEQUALITY IN THE SPHERICAL SPACE WITH APPLICATIONS |
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| YANG Shi-guo,QI Ji-bing and WANG Wen.THE PEDOE INEQUALITY AND ZHANG-YANG INEQUALITY IN THE SPHERICAL SPACE WITH APPLICATIONS[J].Journal of Mathematics,2014,34(1):123-129. |
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| Authors: | YANG Shi-guo QI Ji-bing and WANG Wen |
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| Institution: | YANG Shi-guo;QI Ji-bing;WANG Wen;Department of Mathematical and Center of Research for Teacher and Education,Hefei Normal University;Anhui Xinhua University; |
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| Abstract: | In this paper, we study the problems about geometric inequalities for ndimensional simplexes and finite point sets in the n-dimensional spherical space by theory and method of distance geometry. A form of Pedoe inequality for n-dimensional simplexes and a form of Zhang-Yang inequality for finite point sets in the spherical space are established. From this we obtain the Veljan-Korchmaros inequality and the Finsler-Hadwinger inequality in the n-dimensional spherical space. |
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| Keywords: | spherical space simplex finite point sets geometric inequality |
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