## Abstract This paper investigates the Schur multiplicative and harmonic convexities of the complete symmetric function \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$F\_n(x,r)=\sum \_{i\_1+i\_2+\cdots +i\_n=r}x\_1^{i\_1}x\_2^{i\_2}\ldots x\_n^{i\_n}$\end{document} an
The Schur-convexity of the mean of a convex function
β Scribed by Huan-Nan Shi; Da-Mao Li; Chun Gu
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 391 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
The Schur-convexity at the upper and lower limits of the integral for the mean of a convex function is researched. As applications, a form with a parameter of Stolarsky's mean is obtained and a relevant double inequality that is an extension of a known inequality is established.
π SIMILAR VOLUMES
## Abstract The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions __f__ and __g__ over a convex set __X__. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound
The Schur Horn Convexity Theorem states that for where p denotes the projection on the diagonal. In this paper we generalize this result to the setting of arbitrary separable Hilbert spaces. It turns out that the theorem still holds, if we take the l -closure on both sides. We will also give a desc