| 几何凸(凹)函数积分的上(下)界比较及其一般结果 |
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| 引用本文： | 杨镇杭.几何凸(凹)函数积分的上(下)界比较及其一般结果[J].大学数学,2012(4):76-80. |
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| 作者姓名： | 杨镇杭 |
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| 作者单位： | 浙江省电力试验研究院 |
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| 摘 要： | 运用齐次函数的分析性质,在基本不等式中插入了一个齐次加权"平均",推广加细了基本不等式.作为特例,得到了加权的对数,指数平均不等式,从而部分解决了文1]提出的问题.
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| 关 键 词： | 几何凸函数 齐次函数 加权对数平均 基本不等式 上下界 |
Comparison of Upper(Lower) Bounds for Integral of Geometrically Convex(Concave) Functions and General Results |
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| YANG Zhen-hang.Comparison of Upper(Lower) Bounds for Integral of Geometrically Convex(Concave) Functions and General Results[J].College Mathematics,2012(4):76-80. |
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| Authors: | YANG Zhen-hang |
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| Institution: | YANG Zhen-hang(Zhejiang Province Electric Power Test and Research Institute,Hangzhou 310014,China) |
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| Abstract: | Using the analytic properties of homogeneous functions,a homogeneous weighted mean is inserted in basic inequality,which generalizes and refines the basic inequality.As special examples,the inequalities for weighted logarithmic mean and exponential mean are presented,consequently a part of problems in article 1] is resolved. |
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| Keywords: | geometrically convex functions homogeneous functions weighted logarithmic mean basic inequality upper and lower bounds |
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