Sharp bounds for Toader mean in terms of arithmetic and second contraharmonic means
type: Item
instance of: scholarly article
title: Sharp bounds for Toader mean in terms of arithmetic and second contraharmonic means
zbMATH Open document ID: 1326.26055
DOI: 10.1155/2015/452823
author: Weimao Qian
author: Ying-Qing Song
author: Yu-Ming Chu
author: Xiaohui Zhang
published in: Journal of Function Spaces
publication date: 2015-10-27T00:00:00Z
review text: Summary: We present the best possible parameters \(\lambda_1,\mu_1\in \mathbb{R}\) and \(\lambda_2,\mu_2\in(1/2,1)\) such that double inequalities \(\lambda_1C(a,b)+(1-\lambda_1)A(a,b)<T(a,b)<\mu_1C(a,b)+(1-\mu_1)A(a,b)\), \(C[\lambda_2a+(1-\lambda_2)b,\lambda_2b+(1-\lambda_2)a]<T(a,b)<C[\mu_2a+(1-\mu_2)b,\mu_2b+(1-\mu_2)a]\) hold for all \(a,b>0\) with \(a\neq b\), where \(A(a,b)=(a+b)/2\), \(C(a,b)=(a^3+b^3)/(a^2+b^2)\) and \(T(a,b)=2\int_0^{n/2}\sqrt{a^2\cos^2\theta+b^2\sin^2\theta}d\theta/\pi\) are the arithmetic, second contraharmonic, and Toader means of \(a\) and \(b\), respectively.
Mathematics Subject Classification ID: 26E60
zbMATH DE Number: 6499106
Wikidata QID: Q59112824
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/452823
OpenAlex ID: W1837850567
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description: scientific article; zbMATH DE number 6499106