# Bounds for Toader Mean in Terms of Arithmetic and Second Seiffert Means

## Authors

• Zai-Yin He College of Mathematics and Econometrics, Hunan University, Changsha 410082
• Yue-Ping Jiang College of Mathematics and Econometrics, Hunan University, Changsha 410082
• Yu-Ming Chu Department of Mathematics, Huzhou University, Huzhou 313000

## Keywords:

Toader mean, Second Seiffert mean, Arithmetic mean

## Abstract

In the article, we prove that the double inequalities
\begin{align*}
&\alpha_{1}T(a,b)+(1-\alpha_{1})A(a,b)<TD(a,b)<\beta_{1}T(a,b)+(1-\beta_{1})A(a,b),\\
&T^{\alpha_{2}}(a,b)A^{1-\alpha_{2}}(a,b)<TD(a,b)<T^{\beta_{2}}(a,b)A^{1-\beta_{2}}(a,b)
\end{align*}
hold for all $$a,b>0$$ with $$a\neq b$$ if and only if $$\alpha_{1}\leq 3/4$$, $$\beta_{1}\geq1$$, $$\alpha_{2}\leq 3/4$$ and $$\beta_{2}\geq 1$$,
where $$A(a,b)$$, $$TD(a,b)$$ and $$T(a,b)$$ are the arithmetic, Toader and second Seiffert means of $$a$$ and $$b$$, respectively.

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30-09-2019
CITATION

## How to Cite

He, Z.-Y., Jiang, Y.-P., & Chu, Y.-M. (2019). Bounds for Toader Mean in Terms of Arithmetic and Second Seiffert Means. Communications in Mathematics and Applications, 10(3), 561–570. https://doi.org/10.26713/cma.v10i3.1200

Research Article