| 凸函数与不等式 |
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| 引用本文： | 邓卫兵.凸函数与不等式[J].哈尔滨商业大学学报(自然科学版),2005,21(4):515-517. |
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| 作者姓名： | 邓卫兵 |
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| 作者单位： | 株洲工学院,湖南,株洲,412008 |
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| 摘 要： | 凸性是一种重要的几何性质，凸函数是一种性质特殊的函数，凸集和凸函数在泛函分析、最优化理论、数理经济学等领域都有着广泛的应用，凸函数也是高等数学中的一个基本内容，它在证明比较复杂的不等式方面有着重大作用，探讨了凸函数与不等式之间的密切关系，利用函数的凸性来研究不等式，比传统方法更简洁，还进一步探讨了Jensen不等式的一些具体应用。
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| 关 键 词： | 凸函数 Jensen不等式 不等式的研究 证明 |
| 文章编号： | 1672-0946(2005)04-0515-02 |
| 修稿时间： | 2004年6月30日 |
Function of convexity and inequality |
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| DENG Wei-Bing.Function of convexity and inequality[J].Journal of Harbin University of Commerce :Natural Sciences Edition,2005,21(4):515-517. |
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| Authors: | DENG Wei-Bing |
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| Abstract: | Convexity is an important geometric property, The convex function is a kind of function with special properties. Convexity and convex function have extensive applications in functional analysis, optimal theory, and mathematical economy. Convex function is also a basic content of higher maths, It plays an important role in proving more complex inequality. In this paper, a relation of convex function and inequality of Jensen is studied, it provides an easy way by using the convexity of function to study the inequality and discuss some typical case of inequality of Jensen. |
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| Keywords: | function of convexity inequality of Jensen study of inequality prove |
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