Geodesic
An Inequality for Elementary Symmetric Functions
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 133-135

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Let E r 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 thenwe 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. 
Menon, K. V. An Inequality for Elementary Symmetric Functions. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 133-135. doi: 10.4153/CMB-1972-024-4
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[1] 1. Beckenbach, E. F. and Bellman, R., Inequalities, Springer-Verlag, New York, 1965. Google Scholar

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