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2011•Abstract and Applied AnalysisOpen access

Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean

Hongya Gao, Jianling Guo, Wanguo Yu

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Abstract

For 1 < r < + ∞ , we find the least value α and the greatest value β such that the inequality H α ( a , b ) < A r ( a , b ) < H β ( a , b ) holds for all a , b > 0 with a ≠ b . Here, H ω ( a , b ) and A r ( a , b ) are the generalized Heronian and the power means of two positive numbers a and b , respectively.

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For 1 < r < + ∞ , we find the least value α and the greatest value β such that the inequality H α ( a , b ) < A r ( a , b ) < H β ( a , b ) holds for all a , b > 0 with a ≠ b . Here, H ω ( a , b ) and A r ( a , b ) are the generalized Heronian and the power means of two positive numbers a and b , respectively.

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Available abstract

For 1 < r < + ∞ , we find the least value α and the greatest value β such that the inequality H α ( a , b ) < A r ( a , b ) < H β ( a , b ) holds for all a , b > 0 with a ≠ b . Here, H ω ( a , b ) and A r ( a , b ) are the generalized Heronian and the power means of two positive numbers a and b , respectively.

Key concepts: Algorithm, Computer science

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