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Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean

Author

Listed:
  • Hongya Gao
  • Jianling Guo
  • Wanguo Yu

Abstract

For 1 0 with a ≠ b. Here, Hω(a, b) and Ar(a, b) are the generalized Heronian and the power means of two positive numbers a and b, respectively.

Suggested Citation

  • Hongya Gao & Jianling Guo & Wanguo Yu, 2011. "Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:679201
    DOI: 10.1155/2011/679201
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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. Edward Neuman & József Sándor, 2003. "On certain means of two arguments and their extensions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-13, January.
    3. 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).
    4. 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).
    5. 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).
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Ladislav Matejíčka, 2013. "Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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