Schur Convexity and Inequalities for a Multivariate Symmetric Function. (10th July 2020) - Sun, Ming-Bao; Li, Xin-Ping; Tang, Sheng-Fang; Zhang, Zai-Yun
Abstract : In the article, we provide the Schur, Schur multiplicative, and Schur harmonic convexities properties for the symmetry function F n x, r = F n x 1, x 2, ⋯, x n ; r = ∏ 1 ≤ i 1 < i 2 < ⋯ < i r ≤ n ∑ j = 1 r x i j / 1 − x i j 1 / r on 0, 1 n and find several new analytical inequalities by use of the majorization theory, where x = x 1, ⋯, x n ∈ 0, 1 n, r = 1, 2, ⋯, n and i 1, i 2, ⋯, i n are positive integers.