IJPAM: Volume 102, No. 4 (2015)

OPTIMAL CONVEX COMBINATION BOUNDS OF
GEOMETRIC AND SECOND SEIFFERT MEANS
FOR NEUMAN-SÁNDOR MEAN

Liu Chunrong$^1$, Shi Mingyu$^2$
$^{1,2}$College of Mathematics and Information Science
Hebei University
Baoding, 071002, P.R. CHINA


Abstract. In this paper, we present the least value $\alpha$ and the greatest value $\beta$ such that the double inequality

\begin{displaymath}
\alpha G(a,b)+(1-\alpha)T(a,b)<M(a,b)<\beta G(a,b)+(1-\beta)T(a,b)
\end{displaymath}

holds for all $a,b>0$ with $a\neq b$, where $G(a,b), M(a,b)$ and $T(a,b)$ are respectively the geometric, Neuman-Sándor and second Seiffert means of $a$ and $b$.

Received: January 19, 2015

AMS Subject Classification: 26D15

Key Words and Phrases: inequality, Neuman-Sándor mean, Seiffert mean, geometric mean

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DOI: 10.12732/ijpam.v102i4.7 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 102
Issue: 4
Pages: 671 - 685


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