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Best Possible Bounds for Neuman‐Sándor Mean by the Identric, Quadratic and Contraharmonic Means

Author

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  • Tie-Hong Zhao
  • Yu-Ming Chu
  • Yun-Liang Jiang
  • Yong-Min Li

Abstract

We prove that the double inequalities Iα1(a,b)Q1-α1(a,b) 0 with a ≠ b if and only if α1 ≥ 1/2, β1≤log [2log (1+2)]/(1-log 2), α2 ≥ 5/7, and β2≤log [21log (+2)], where I(a, b), M(a, b), Q(a, b), and C(a, b) are the identric, Neuman‐Sándor, quadratic, and contraharmonic means of a and b, respectively.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:348326
    DOI: 10.1155/2013/348326
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    References listed on IDEAS

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    1. Yu-Ming Chu & Shou-Wei Hou, 2012. "Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-6, December.
    2. Yu-Ming Chu & Miao-Kun Wang & Zi-Kui Wang, 2011. "A Sharp Double Inequality between Harmonic and Identric Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    3. Yu-Ming Chu & Bo-Yong Long, 2013. "Bounds of the Neuman‐Sándor Mean Using Power and Identric Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Yu-Ming Chu & Miao-Kun Wang & Zi-Kui Wang, 2011. "A Sharp Double Inequality between Harmonic and Identric Means," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-7, October.
    5. 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).
    6. Tie-Hong Zhao & Yu-Ming Chu & Bao-Yu Liu, 2012. "Optimal Bounds for Neuman-Sándor Mean in Terms of the Convex Combinations of Harmonic, Geometric, Quadratic, and Contraharmonic Means," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, December.
    7. Yu-Ming Chu & Bo-Yong Long, 2013. "Bounds of the Neuman-Sándor Mean Using Power and Identric Means," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, February.
    8. Tie-Hong Zhao & Yu-Ming Chu & Bao-Yu Liu, 2012. "Optimal Bounds for Neuman‐Sándor Mean in Terms of the Convex Combinations of Harmonic, Geometric, Quadratic, and Contraharmonic Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. Wei-Mao Qian & Yu-Ming Chu, 2013. "On Certain Inequalities for Neuman‐Sándor Mean," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Fan Zhang & Yu-Ming Chu & Wei-Mao Qian, 2013. "Bounds for the Arithmetic Mean in Terms of the Neuman‐Sándor and Other Bivariate Means," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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