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A Sharp Double Inequality between Harmonic and Identric Means

Author

Listed:
  • Yu-Ming Chu
  • Miao-Kun Wang
  • Zi-Kui Wang

Abstract

We find the greatest value p and the least value q in (0,1/2) such that the double inequality H(pa + (1 − p)b, pb + (1 − p)a) 0 with a ≠ b. Here, H(a, b), and I(a, b) denote the harmonic and identric means of two positive numbers a and b, respectively.

Suggested Citation

  • Yu-Ming Chu & Miao-Kun Wang & Zi-Kui Wang, 2011. "A Sharp Double Inequality between Harmonic and Identric Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:657935
    DOI: 10.1155/2011/657935
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    References listed on IDEAS

    as
    1. Yu-Ming Chu & Bo-Yong Long, 2010. "Best Possible Inequalities between Generalized Logarithmic Mean and Classical Means," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-13, March.
    2. Yu-Ming Chu & Shan-Shan Wang & Cheng Zong, 2011. "Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    3. Yu-Ming Chu & Bo-Yong Long, 2010. "Best Possible Inequalities between Generalized Logarithmic Mean and Classical Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
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    Cited by:

    1. Yu-Ming Chu & Bo-Yong Long, 2013. "Bounds of the Neuman‐Sándor Mean Using Power and Identric Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Tie-Hong Zhao & Yu-Ming Chu & Yun-Liang Jiang & Yong-Min Li, 2013. "Best Possible Bounds for Neuman‐Sándor Mean by the Identric, Quadratic and Contraharmonic Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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