{"title":"A double inequality for the combination of Toader mean and the arithmetic mean in terms of the contraharmonic mean","authors":"Weidong Jiang, Feng Qi (祁锋)","doi":"10.2298/PIM141026009J","DOIUrl":null,"url":null,"abstract":"We find the greatest value λ and the least value μ such that the double \n inequality C(λa +(1-λ)b, λb + (1-λ)a) < αA(a,b) + (1-α)T(a, b)< \n C(μa + (1-μ)b, μb + (1-μ)a) holds for all α (0,1) and a, b > 0 with \n a ≠ b, where C(a,b), A(a,b), and T(a,b) denote respectively the \n contraharmonic, arithmetic, and Toader means of two positive numbers a and \n b.","PeriodicalId":416273,"journal":{"name":"Publications De L'institut Mathematique","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2014-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Publications De L'institut Mathematique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/PIM141026009J","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 7
Abstract
We find the greatest value λ and the least value μ such that the double
inequality C(λa +(1-λ)b, λb + (1-λ)a) < αA(a,b) + (1-α)T(a, b)<
C(μa + (1-μ)b, μb + (1-μ)a) holds for all α (0,1) and a, b > 0 with
a ≠ b, where C(a,b), A(a,b), and T(a,b) denote respectively the
contraharmonic, arithmetic, and Toader means of two positive numbers a and
b.
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