| 对一道积分不等式题的再思考 |
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| 引用本文： | 刘海峰.对一道积分不等式题的再思考[J].数学学习,2011(2):20-21,30. |
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| 作者姓名： | 刘海峰 |
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| 作者单位： | 上海海洋大学信息学院,上海201306 |
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| 基金项目： | 上海高校选拔培养优秀青年教师科研专项基金. |
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| 摘 要： | 利用提升维度的方法并结合几何图形直观分析,给出一道一元函数积分均值不等式的新证明,并将原不等式推广至形式较为对称的不等式,使得原不等式成为新不等式的特例.最后证明新不等式与函数单调递减的定义等价.
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| 关 键 词： | 积分均值 积分不等式 单调递减函数 |
Revisiting an Integral Inequality |
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| LIU Hai-feng.Revisiting an Integral Inequality[J].Studies In College Mathematics,2011(2):20-21,30. |
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| Authors: | LIU Hai-feng |
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| Institution: | LIU Hai-feng (School of Information Technology, Shanghai Ocean University, Shanghai 201306, PRC ) |
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| Abstract: | A new proof of an integral mean value inequality is given by lifting the dimension of the variable space. The original inequality is generalized to a new inequality in a symmetry form. It is proved also that the new inequality is equivalent to the decreasingness of＇the related function. |
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| Keywords: | integral mean value integral inequality monotone decreasing function |
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