Newton's Inequalities Research Articles

Normalized Symmetric Functions, Newton's Inequalities, and a New Set of Stronger Inequalities

(1989). Normalized Symmetric Functions, Newton's Inequalities, and a New Set of Stronger Inequalities. The American Mathematical Monthly: Vol. 96, No. 9, pp. 815-819.

Normalized Symmetric Functions, Newton's Inequalities, and a New Set of Stronger Inequalities

Normalized Symmetric Functions, Newton's Inequalities, and a New Set of Stronger Inequalities

Newton's Inequality and a Test for Imaginary Roots

Newton's Inequality and a Test for Imaginary Roots

An Inequality for Elementary Symmetric Functions

Let Er denote the rth elementary symmetric function on α1 α2,…,αm which is defined by1E0 = 1 and Er=0(r>m).We define the rth symmetric mean by2where denote the binomial coefficient. If α1 α2,…,αm are positive reals thenwe have two well-known inequalities3and4In 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.

On Newton's Inequality for Real Polynomials

(1969). On Newton's Inequality for Real Polynomials. The American Mathematical Monthly: Vol. 76, No. 8, pp. 905-909.

On Newton's Inequality for Real Polynomials

On Newton's Inequality for Real Polynomials

An inequality of Schur and an inequality of Newton

2 (1.3) Er ? Er-iEr+1 and (1.4) 1r ? Hr-lHr+i. 1 The inequality (1.3) is known as Newton's inequality and is true when a1, a2, * * *, am are real numbers. The inequality (1.4), given by Professor Schur, is true when a1, a2, * * X am are nonnegative reals. In [1], Whiteley has given the following generalizations of (1.3) and (1.4): Let (1.5) El(K) = Xi1,2* *,anOl Of2 . . . a.m e i + i2 + ***+ im =r, /K = (1)