A simple proof of inequalities related to means

Authors

  • Gou-Sheng Yang
  • Shuoh-Jung Liu

DOI:

https://doi.org/10.5556/j.tkjm.40.2009.606

Abstract

The purpose of this paper is to give a fairly elementary method to prove that the function $u(\alpha)=[\frac{x^{\alpha}-y^{\alpha}}{\alpha(x-y)}]^{\frac{1}{\alpha -1}},$ $\alpha \neq 0,1, u(0)=I, u(1)=L, $ is strictly increasing, and to give a simple proof of the inequalities $x

Author Biographies

Gou-Sheng Yang

Department of Mathematics Tamkang University, Tamsui 25137, Taiwan, Republic of China.

Shuoh-Jung Liu

Department of Mathematics Tamkang University, Tamsui 25137, Taiwan, Republic of China.

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Published

2009-12-23

How to Cite

Yang, G.-S., & Liu, S.-J. (2009). A simple proof of inequalities related to means. Tamkang Journal of Mathematics, 40(4), 429-436. https://doi.org/10.5556/j.tkjm.40.2009.606

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Section

Papers

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