| 关于Jensen不等式中的思想方法 |
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| 引用本文： | 付夕联,包芳勋.关于Jensen不等式中的思想方法[J].曲阜师范大学学报,1993,19(3):79-82. |
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| 作者姓名： | 付夕联 包芳勋 |
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| 作者单位： | 曲阜师范大学科学方法论研究中心，曲阜师范大学科学方法论研究中心，曲阜师范大学科学方法论研究中心，曲阜师范大学科学方法论研究中心 273165 山东省曲阜市，273165 山东省曲阜市，273165 山东省曲阜市，273165 山东省曲阜市 |
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| 摘 要： | 分析了Jensen不等式的来胧去脉,指出,在Jensen基本不等式的形成过程中,渗透着观察、类比联想、归纳、猜想等思想方法;而由Jensen基本不等式中的均等性联想到非均等性,则导致了Jensen总和不等式的产生;由Jensen总和不等式中变量的离散性联想到变量的连续性,则导致Jensen积分不等式的发现。
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| 关 键 词： | 均等性 离散性 连续性 Jensen不等式 凸函数 |
ON THE MENTALITY OF JENSEN INEQUALITY |
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| Fu Xilian Bao Fangxun Zhang Zhaosheng Zhang Yufeng Center of Scientific Methodology Reach,Qufu Normal University,Qufu,Shandong,PRC.ON THE MENTALITY OF JENSEN INEQUALITY[J].Journal of Qufu Normal University(Natural Science),1993,19(3):79-82. |
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| Authors: | Fu Xilian Bao Fangxun Zhang Zhaosheng Zhang Yufeng Center of Scientific Methodology Reach Qufu Normal University Qufu Shandong PRC |
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| Institution: | Fu Xilian Bao Fangxun Zhang Zhaosheng Zhang Yufeng Center of Scientific Methodology Reach,Qufu Normal University,273165,Qufu,Shandong,PRC |
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| Abstract: | The origin and developmant of Jensen inequality is analysed. It is pointed out that the mentality, such as observation, analogy association, induction, guess permeates through the course of forming Jensen basic inequa lity. Associating the disproporlionality from the proportionality in Jensen basic inequality leads to the generation of Jensen summation inequality. Associating the continuous variable from the discrete variable in Jensen summation inequality leads to the discovery of Jensen integral inequality. |
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| Keywords: | analogy association proportionality discretion continuity |
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