Mixed-mean inequalities for subsets期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Mixed-mean inequalities for subsets

Authors:	Gangsong Leng Lin Si Qingsan Zhu

Affiliation:	Department of Mathematics, Shanghai University, Shanghai, 200436, People's Republic of China ; Department of Mathematics, Shanghai University, Shanghai, 200436, People's Republic of China ; School of Mathematical Sciences, Peking University, Beijing 100871, People's Republic of China

Abstract:	For $Asubset X={x_1,...,x_n ~vert~x_igeq 0, ~i=1,2,...,n},$ let and denote the arithmetic mean and geometric mean of elements of , respectively. It is proved that if is an integer in $(frac{n}{2}, n]$ , then $begin{displaymath}Big(prod_{vert Avert=katop Asubset X}a_{A}Big)^{frac{... ...{1}{C_n^k}Big(sum_{vert Avert=katop Asubset X}g_{A}Big),end{displaymath}$ with equality if and only if . Furthermore, as a generalization of this inequality, a mixed power-mean inequality for subsets is established.

Keywords:	Mixed mean power mean Carlson inequality

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载全文