Nonlinear Sherman-type inequalities-Reference-Cited by-同舟云学术

Nonlinear Sherman-type inequalities

Published:2018-09-21 Issue:1 Volume:9 Page:168-175
ISSN:2191-950X
Container-title:Advances in Nonlinear Analysis
language:en
Short-container-title:

Author:

Niezgoda Marek¹

Affiliation:

1. Department of Applied Mathematics and Computer Science , University of Life Sciences in Lublin , Akademicka 15, 20-950 Lublin , Poland

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Subject

Analysis

Reference17 articles.

1. M. Adil Khan, S. Ivelić Bradanović and J. Pečarić, On Sherman’s type inequalities for n-convex function with applications, Konuralp J. Math. 4 (2016), no. 2, 255–270.

2. M. Adil Khan, J. Khan and J. Pečarić, Generalizations of Sherman’s inequality by Montgomery identity and Green function, Electron. J. Math. Anal. Appl. 5 (2017), no. 1, 1–16.

3. R. P. Agarwal, S. Ivelić Bradanović and J. Pečarić, Generalizations of Sherman’s inequality by Lidstone’s interpolating polynomial, J. Inequal. Appl. 2016 (2016), 10.1186/s13660-015-0935-6.

4. A.-M. Burtea, Two examples of weighted majorization, An. Univ. Craiova Ser. Mat. Inform. 37 (2010), no. 2, 92–99.

5. M. L. Eaton, On group induced orderings, monotone functions, and convolution theorems, Inequalities in statistics and probability (Lincoln 1982), IMS Lecture Notes Monogr. Ser. 5, Institute of Mathematical Statistics, Hayward (1984), 13–25.

Cited by 11 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. n-convexity and weighted majorization with applications to f-divergences and Zipf–Mandelbrot law;Periodica Mathematica Hungarica;2024-07-03

2. New Versions of Uniformly Convex Functions via Quadratic Complete Homogeneous Symmetric Polynomials;Mediterranean Journal of Mathematics;2023-08-18

3. The Hardy–Littlewood–Pólya inequality of majorization in the context of $$\mathbf {\omega }$$–$$\textbf{m}$$–star-convex functions;Aequationes mathematicae;2023-02-11

4. On generalized Csiszár (f,g)-divergence with an application for p-majorization;Mathematical Inequalities & Applications;2023

5. Sherman's functional, its properties with applications for f-divergence measure;Mathematical Inequalities & Applications;2023