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Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean

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  • Yu-Ming Chu
  • Shou-Wei Hou

Abstract

We find the greatest value α and the least value β in (1/2, 1) such that the double inequality C(αa + (1 − α)b, αb + (1 − α)a) 0 with a ≠ b. Here, T(a, b) = (a − b)/[2 arctan((a − b)/(a + b))] and C(a, b) = (a2 + b2)/(a + b) are the Seiffert and contraharmonic means of a and b, respectively.

Suggested Citation

  • Yu-Ming Chu & Shou-Wei Hou, 2012. "Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:425175
    DOI: 10.1155/2012/425175
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    References listed on IDEAS

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    1. Yu-Ming Chu & Miao-Kun Wang & Song-Liang Qiu & Ye-Fang Qiu, 2011. "Sharp Generalized Seiffert Mean Bounds for Toader Mean," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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    Cited by:

    1. Hui Sun & Ying-Qing Song & Yu-Ming Chu, 2013. "Optimal Two Parameter Bounds for the Seiffert Mean," Journal of Applied Mathematics, 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).
    3. Zai-Yin He & Wei-Mao Qian & Yun-Liang Jiang & Ying-Qing Song & Yu-Ming Chu, 2013. "Bounds for the Combinations of Neuman‐Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).

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