Schur convexity and Schur multiplicative convexity for a class of symmetric functions with applications

• Date: 2009
• Main Authors: Wei-feng, Xia, Вей, Фен-Ся
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3102
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For $x = (x_1, x_2, …, x_n) ∈ (0, 1 ]^n$ and $r ∈ \{ 1, 2, … , n\}$, a symmetric function $F_n(x, r)$ is defined by the relation $$F_n(x,r) = F_n(x_1, x_2, …, x_n; r) = ∑_{1 ⩽ i_1 < i_2…i_r ⩽n } ∏^r_{j=1}\frac{1−x_{i_j}}{x_{i_j}},$$ where $i_1 , i_2 , ... , i_n$ are positive integers. This pa...