EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 99(113), pp. 237–242 (2016)

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A DOUBLE INEQUALITY FOR THE COMBINATION OF TOADER MEAN AND THE ARITHMETIC MEAN IN TERMS OF THE CONTRAHARMONIC MEAN

Wei-Dong Jiang, Feng Qi

College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, China; Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, China; Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, China

Abstract: We find the greatest value $\lambda$ and the least value $\mu$ such that the double inequality \begin{align*} C(\lambda a+(1-\lambda)b,\lambda b+(1-\lambda)a)&<\alpha A(a,b)+(1-\alpha)T(a,b)
&<C(\mu a+(1-\mu)b,\mu b+(1-\mu)a) \end{align*} holds for all $\alpha\in(0,1)$ and $a,b>0$ with $a\neq b$, 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 $b$.

Keywords: bound; contraharmonic mean; arithmetic mean; Toader mean; complete elliptic integrals

Classification (MSC2000): 26E60; 33E05

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Electronic fulltext finalized on: 12 Apr 2016. This page was last modified: 20 Apr 2016.

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