Schur \(m\)-power convexity of a class of multiplicatively convex functions and applications
type: Item
instance of: scholarly article
title: Schur \(m\)-power convexity of a class of multiplicatively convex functions and applications
zbMATH Open document ID: 1470.26019
DOI: 10.1155/2014/258108
author: W. Wang
author: Shiguo Yang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We investigate the conditions under which the symmetric functions \(F_{n, k}(\mathbf{x}, r) = \prod_{1 \leq i_1 < i_2 < \cdots < i_k \leq n} f \left((\sum_{j = 1}^k x_{i_j}^r)^{1 / r}\right)\), \(k = 1,2, \dots, n\), are Schur \(m\)-power convex for \(x \in \mathbb{R}_{+ +}^n\) and \(r > 0\). As a consequence, we prove that these functions are Schur geometrically convex and Schur harmonically convex, which generalizes some known results. By applying the theory of majorization, several inequalities involving the \(p\)th power mean and the arithmetic, the geometric, or the harmonic means are presented.
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 05E05
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 7022017
Wikidata QID: Q59037061
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/258108
OpenAlex ID: W2017345085
cites work: Q4441514
cites work: A refinement of various mean inequalities
cites work: A class of symmetric functions for multiplicatively convex function
cites work: Q3569782
cites work: Q3144262
cites work: Schur-convexity of dual form of some symmetric functions
cites work: Schur power convexity of Stolarsky means
cites work: Schur power convexity of Gini means
cites work: Schur power convexity of the Daróczy means
cites work: Schur \(m\)-power convexity of generalized Hamy symmetric function
cites work: Q5497876
cites work: Inequalities: theory of majorization and its applications
cites work: The Schur harmonic convexity for a class of symmetric functions
cites work: Schur-harmonic convexity for differences of some means
cites work: Convexity according to the geometric mean
cites work: Q4901111
cites work: Generalization and sharpness of the power means inequality and their applications
cites work: Q5254252
cites work: Inequalities for symmetric means, symmetric harmonic means, and their applications
cites work: The Hamy symmetric function and its generalization
cites work: Schur convexity for a class of symmetric functions
cites work: Notes on the Schur-convexity of the extended mean values
cites work: Generalized convexity and inequalities
cites work: Q3391719
cites work: Q3540845
cites work: Schur-convexity for a class of symmetric functions and its applications
cites work: Parametric Schur convexity and arrangement monotonicity properties of partial sums
cites work: Schur-convexity and Schur-geometrically concavity of Gini means
cites work: Q4743587
cites work: Necessary and sufficient condition for Schur convexity of the two-parameter symmetric homogeneous means
cites work: Necessary and sufficient conditions for Schur geometrical convexity of the four-parameter homogeneous means
cites work: Q3097060
cites work: Q3994523
cites work: Inequalities for a simplex and an interior point
cites work: Q5299667
cites work: Schur convex functions and inequalities of \(n\)-simplex
description: scientific article; zbMATH DE number 7022017