| 关于双曲函数的两个平均及其Schur凸性 |
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| 引用本文： | 李明,何灯. 关于双曲函数的两个平均及其Schur凸性[J]. 湖州师专学报, 2011, 0(1): 11-14 |
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| 作者姓名： | 李明 何灯 |
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| 作者单位： | [1]中国医科大学数学教研室,辽宁沈阳110001 [2]福清港头中学,福建福清350317 |
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| 摘 要： | 通过类比三角函数的两个平均,定义了双曲函数的两个平均Msh（a,b）和Mth（a,b）.为进一步确定它们的Schur凸性,采用了凸函数的相关理论,并结合Hadamard不等式,证明出Msh（a,b）在[0,＋∞）上为Schur凸函数,而Mth（a,b）在[0,＋∞）上为Schur凹函数.基于这两个平均的Schur凸性,建立了一个涉及算术平均、Msh（a,b）和Mth（a,b）的新不等式链.
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| 关 键 词： | 双曲函数 Schur凸性 Hadamard不等式 不等式链 |
On the Two Means of Hyperbolic Functions and Their Schur Convexity |
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| LI Ming,HE Deng. On the Two Means of Hyperbolic Functions and Their Schur Convexity[J]. , 2011, 0(1): 11-14 |
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| Authors: | LI Ming HE Deng |
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| Affiliation: | 1. Teaching ＆ Research Group of Mathematics, China Medical University, Shenyang 110001, China 2. Fuqing Gangtou Middle School, Fuqing 350305, China) |
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| Abstract: | Through the analogy of the two means of trigonometric functions,this article defines two means of hyperbolic functions Msh（a,b） and Mth（a,b）.In order to determine their Schur convexity,this article takes advantage of the theory about the convex functions and the Hadamard’s inequality to find out that Msh（a,b） is Schur convexity and Mth（a,b） is Schur concavity.Finally,based on the Schur convexity of the two means,this article establishes a new inequality chain which contains arithmetic mean,Msh（a,b） and Mth（a,b）. |
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| Keywords: | hyperbolic function Schur convexity Hadamard＇s inequality inequality chain |
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