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Optimal Inequalities for Power Means

Author

Listed:
  • Yong-Min Li
  • Bo-Yong Long
  • Yu-Ming Chu
  • Wei-Ming Gong

Abstract

We present the best possible power mean bounds for the product Mpα(a,b)M-p1-α(a,b) for any p > 0, α ∈ (0,1), and all a, b > 0 with a ≠ b. Here, Mp(a, b) is the pth power mean of two positive numbers a and b.

Suggested Citation

  • Yong-Min Li & Bo-Yong Long & Yu-Ming Chu & Wei-Ming Gong, 2012. "Optimal Inequalities for Power Means," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:182905
    DOI: 10.1155/2012/182905
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    References listed on IDEAS

    as
    1. 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).
    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, Hindawi, vol. 2011, pages 1-9, July.
    3. Yu-Ming Chu & Ye-Fang Qiu & Miao-Kun Wang, 2010. "Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-12, September.
    4. Wei-Feng Xia & Yu-Ming Chu & Gen-Di Wang, 2010. "The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    5. Ming-yu Shi & Yu-ming Chu & Yue-ping Jiang, 2009. "Optimal Inequalities among Various Means of Two Arguments," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    6. Yu-Ming Chu & Ye-Fang Qiu & Miao-Kun Wang, 2010. "Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    7. Ming-yu Shi & Yu-ming Chu & Yue-ping Jiang, 2009. "Optimal Inequalities among Various Means of Two Arguments," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-10, November.
    8. Wei-Feng Xia & Yu-Ming Chu & Gen-Di Wang, 2010. "The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-9, April.
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