Chu, Yu-Ming; Hou, Shou-Wei; Shen, Zhong-Hua Sharp bounds for Seiffert mean in terms of root mean square. (English) Zbl 1275.26051 J. Inequal. Appl. 2012, Paper No. 11, 6 p. (2012). Summary: We find the greatest value \(\alpha\) and least value \(\beta\) in \((1/2,1)\) such that the double inequality \[ S(\alpha a+(1-\alpha)b,\alpha b+(1-\alpha)a)<T(a,b)< S(\beta a+(1-\beta)b,\beta b+(1-\beta)a) \] holds for all \(a,b>0\) with \(a\neq b\). Here, \(T(a,b)=(a-b)/[2 \arctan((a-b)/(a+b))]\) and \(S(a,b)=[(a^2+b^2)/2]^{1/2}\) are the Seiffert mean and root mean square of \(a\) and \(b\), respectively. Cited in 1 ReviewCited in 5 Documents MSC: 26E60 Means Keywords:Seiffert mean; root mean square; power mean; inequality PDFBibTeX XMLCite \textit{Y.-M. Chu} et al., J. Inequal. Appl. 2012, Paper No. 11, 6 p. (2012; Zbl 1275.26051) Full Text: DOI References: [1] doi:10.1016/j.jco.2003.08.007 · Zbl 1073.65005 · doi:10.1016/j.jco.2003.08.007 [2] doi:10.1063/1.532988 · Zbl 1055.82507 · doi:10.1063/1.532988 [3] doi:10.1139/p80-162 · Zbl 0982.81538 · doi:10.1139/p80-162 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.