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Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean

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  • Hongya Gao
  • Jianling Guo
  • Wanguo Yu

Abstract

For 1 < ð ‘Ÿ < + ∞ , we find the least value ð ›¼ and the greatest value ð ›½ such that the inequality ð » ð ›¼ ( ð ‘Ž , ð ‘ ) < ð ´ ð ‘Ÿ ( ð ‘Ž , ð ‘ ) < ð » ð ›½ ( ð ‘Ž , ð ‘ ) holds for all ð ‘Ž , ð ‘ > 0 with ð ‘Ž â‰ ð ‘ . Here, ð » ð œ” ( ð ‘Ž , ð ‘ ) and ð ´ ð ‘Ÿ ( ð ‘Ž , ð ‘ ) are the generalized Heronian and the power means of two positive numbers ð ‘Ž and ð ‘ , 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, Hindawi, vol. 2011, pages 1-9, June.
    • Handle: RePEc:hin:jnlaaa:679201
    DOI: 10.1155/2011/679201
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