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An Inequality for Elementary Symmetric Functions
Published online by Cambridge University Press: 20 November 2018
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Let Er denote the rth elementary symmetric function on α1 α2,…,αm which is defined by
1
E0 = 1 and Er=0(r>m).
We define the rth symmetric mean by
2
where denote the binomial coefficient. If α1 α2,…,αm are positive reals then
we have two well-known inequalities
3
and
4
In this paper we consider a generalization of these inequalities. The inequality (4) is known as Newton's inequality which contains the arithmetic and geometric mean inequality.
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- Copyright © Canadian Mathematical Society 1972
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