{"title":"Schur convexity properties for a class of symmetric functions with applications","authors":"Wei-Mao Qian, Y. Chu","doi":"10.22436/JNSA.011.06.10","DOIUrl":null,"url":null,"abstract":"In the article, we prove that the symmetric function Fn (x1, x2, · · · , xn; r) = ∑ 16i1<i2<···<ir6n r ∏ j=1 ( 1 + xij 1 − xij )1/r is Schur convex, Schur multiplicatively convex and Schur harmonic convex on [0, 1)n, and establish several new analytic inequalities by use of the theory of majorization, where r ∈ {1, 2, · · · ,n} and i1, i2, · · · in are integers.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"12 1","pages":"841-849"},"PeriodicalIF":0.0000,"publicationDate":"2018-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Nonlinear Sciences and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22436/JNSA.011.06.10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In the article, we prove that the symmetric function Fn (x1, x2, · · · , xn; r) = ∑ 16i1
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