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Bounds for the Combinations of Neuman‐Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean

Author

Listed:
  • Zai-Yin He
  • Wei-Mao Qian
  • Yun-Liang Jiang
  • Ying-Qing Song
  • Yu-Ming Chu

Abstract

We give the greatest values r1, r2 and the least values s1, s2 in (1/2, 1) such that the double inequalities C(r1a + (1 − r1)b, r1b + (1 − r1)a) 0 with a ≠ b, where A(a, b), M(a, b), C(a, b), and T(a, b) are the arithmetic, Neuman‐Sándor, contraharmonic, and second Seiffert means of a and b, respectively.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:903982
    DOI: 10.1155/2013/903982
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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 & Shou-Wei Hou, 2012. "Sharp Bounds for Seiffert Mean in Terms of Contraharmonic Mean," 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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