Optimal bounds for a Toader-type mean in terms of one-parameter quadratic and contraharmonic means

Volume 9, Issue 5, pp 3424--3432 http://dx.doi.org/10.22436/jnsa.009.05.126

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Authors

Hong-Hu Chu - School of Civil Engineering and Architecture, Changsha University of Science & Technology, Changsha 410114, China. Wei-Mao Qian - School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, China. Yu-Ming Chu - School of Mathematics and Computation Science, Hunan City University, Yiyang 413000, China. Ying-Qing Song - School of Mathematics and Computation Science, Hunan City University, Yiyang 413000, China.

Abstract

In this paper, we present the best possible Toader mean bounds of arithmetic and quadratic means by the one-parameter quadratic and contraharmonic means. As applications in engineering and technology, we find new bounds for the complete elliptic integral of the second kind.

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Keywords

• Toader mean
• arithmetic mean
• quadratic mean
• contraharmonic mean
• complete elliptic integral.

MSC

•  26E60
•  33E05

References

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