| 混合加权幂平均不等式的推广 |
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| 引用本文： | 马统一,张海娟.混合加权幂平均不等式的推广[J].上海大学学报(英文版),2006,10(3):192-197. |
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| 作者姓名： | 马统一 张海娟 |
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| 作者单位： | 1. 河西学院
2. 日照职业技术学院 |
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| 基金项目： | Project supported by National Natural Science Foundation ofChina (Grant No .10271071) |
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| 摘 要： | 1 Introduction In 1992 , Holland1]presented an interesting conjec-ture :letx1,x2,…,xnbe positive real numbers . Thearithmetic mean of the numbersx1, (x1x2)21,(x1x2x3)31,…,(x1x2…xn)1ndoes not exceed thegeometric mean of the numbersx1,(x1 2x2),(x1 x2 x3)3, …,(x1 x2 n… xn). There isequalityif and onlyifx1=x2=…=xn. A combinatorial proof of this conjecture was givenby Kedlaya2]and aninductive proof with a little analy-sis was obtained by Matstuda3].Other different proofscan be found in R…
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| 关 键 词： | 不等式 幂均值 差分函数 分离 |
| 文章编号： | 1007-6417（2006）03-0192-06 |
| 收稿时间： | 2005-07-12 |
Generalizations of mixed weighted power mean inequality |
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| Tong-yi Ma,Hai-juan Zhang.Generalizations of mixed weighted power mean inequality[J].Journal of Shanghai University(English Edition),2006,10(3):192-197. |
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| Authors: | Tong-yi Ma Hai-juan Zhang |
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| Institution: | (1) Department of Mathematics, Hexi University, 734000 Zhangye, P.R. China;(2) Five Years Successive Education Department, Rizhao Vocational and Technical College, 276826 Rizhao, P.R. China |
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| Abstract: | Tarnavas established mixed weighted power mean inequality in 1999. A separation of weighted power mean inequality was derived in this paper. As its applications, some separations of other inequalities were given. |
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| Keywords: | inequality power mean weighted power mean mixed weighted power mean difference function of mixed weighted power mean separation |
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