| 利用函数的凸凹性证明均值不等式 |
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| 引用本文： | 鄢凤明.利用函数的凸凹性证明均值不等式[J].湖南人文科技学院学报,2001(4):15-17. |
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| 作者姓名： | 鄢凤明 |
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| 作者单位： | 娄底师范高等专科学校,湖南,娄底,417000 |
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| 摘 要： | 从利用Jensen不等式证明均值不等式关系的过程中函数的取法入手 ,证明了这种不等关系与函数性质 (凸性、单调性 )之间的关系 ,由此可以定义一种更一般的平均———函数平均 ,而调和平均、几何平均、算术平均只是函数平均在特殊函数上的表现
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| 关 键 词： | 均值不等式 函数平均 凸性 单调性 |
| 文章编号： | 1008-1666(2001)04-0015-03 |
| 修稿时间： | 2001年10月8日 |
On the Proof of Inequality of Equal Value by Convexity or Concavity of Function |
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| YAN Feng-ming.On the Proof of Inequality of Equal Value by Convexity or Concavity of Function[J].Journal of Hunan Institute of Humanities,Science and Technology,2001(4):15-17. |
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| Authors: | YAN Feng-ming |
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| Abstract: | From the choice of function in the proof of inequality of equal value by utilizing Jensen's inequality,the author demonstrate the relation between inequality of equal value and properties of function ,and defines the function average which is a more general average.thus thinking harmonic average,geometrical average and arithmetic average are special function's manifestations of function average. |
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| Keywords: | inequality of equal value function average convexity monotonicity |
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