Abstract
For \(0<a<b\), the harmonic, geometric and Holder means satisfy \newline\( H<G<Q\). They are special cases \((p=-1,0,2)\) of power means \(M_{p}\).
We consider the following problem: find all \(\U{3b1} ,\U{3b2} \in R\) for which the bilateral inequalities \(\U{3b1} H(a,b)+(1-\U{3b1} )Q(a,b)<G(a,b)<\U{3b2} H(a,b)+(1-\U{3b2} )Q(a,b)\) hold \(\forall0<a<b\). Then we replace in the bilateral inequalities the mean \(Q\) by \(Mp\), \(p>0\) and address the same problem
Authors
Mira-Cristiana Anisiu
“Tiberiu Popoviciu” Institute of Numerical Analysis Romanian Academy
Valeriu Anisiu
“Babes-Bolyai” University Faculty of Mathematics and Computer Sciences
Keywords
Means; power means; bilateral inequalities
Paper coordinates
M.-C. Anisiu, V. Anisiu, Bilateral inequalities for harmonic, geometric and Hölder means, Stud. Univ. Babes-Bolyai Math., 59 (2014) no. 4, pp. 463-468.
About this paper
Journal
Studia Universitatis Babes-Bolyai, Mathematica
Publisher Name
Babes-Bolyai Univeristy Cluj-Napoca, Romania
Print ISSN
Online ISSN
2065-961x
google scholar link
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