| 凸函数及其在不等式证明中的应用 |
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| 引用本文： | 尚亚东,游淑军. 凸函数及其在不等式证明中的应用[J]. 广州大学学报(自然科学版), 2005, 4(1): 1-6 |
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| 作者姓名： | 尚亚东 游淑军 |
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| 作者单位： | 广州大学,数学与信息科学学院,广东,广州,510405 |
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| 基金项目： | 国家自然科学基金资助项目(10271034) |
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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．借助凸集引入凸函数概念，介绍了凸函数的基本性质，特别研究了凸函数的Jensen不等式在不等式证明中的应用。
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| 关 键 词： | 凸性 凸集 凸函数 Jensen不等式 |
| 文章编号： | 1671-4229(2005)01-0001-06 |
| 修稿时间： | 2004-04-12 |
Convex function and its application in proving inequalities |
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| SHANG Ya-dong,YOU Shu-jun. Convex function and its application in proving inequalities[J]. Journal og Guangzhou University:Natural Science Edition, 2005, 4(1): 1-6 |
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| Authors: | SHANG Ya-dong YOU Shu-jun |
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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. In this paper, we introduce the definition of convex function by the aid of convex set. We discuss some foundational properties of the convex function. Especially, we study the applications of Jensen inequality of convex function in proving inequalities. |
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| Keywords: | convexity convex set convex function Jensen inequality |
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