Nonlinear Sherman-type inequalities

Advances in Nonlinear Analysis

article

Marek Niezgoda¹ 

[1] Department of Applied Mathematics and Computer Science, University of Life Sciences in Lublin

关键词: Majorization;    convex function;    convex-concave map;    HLPK inequality;    Sherman inequality;    directional derivative;    gradient;   

DOI  :  10.1515/anona-2018-0098

学科分类：社会科学、人文和艺术（综合）

来源: De Gruyter

【 摘 要 】

An important class of Schur-convex functions is generated by convex functions via the well-known Hardy–Littlewood–Pólya–Karamata inequality. Sherman’s inequality is a natural generalization of the HLPK inequality. It can be viewed as a comparison of two special inner product expressions induced by a convex function of one variable. In the present note, we extend the Sherman inequality from the (bilinear) inner product to a (nonlinear) map of two vectorial variables satisfying the Leon–Proschan condition. Some applications are shown for directional derivatives and gradients of Schur-convex functions.

【 授权许可】

CC BY