IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2012y2012i1n379785.html

A Best Possible Double Inequality for Power Mean

Author

Listed:
  • Yong-Min Li
  • Bo-Yong Long
  • Yu-Ming Chu

Abstract

We answer the question: for any p, q ∈ ℝ with p ≠ q and p ≠ −q, what are the greatest value λ = λ(p, q) and the least value μ = μ(p, q), such that the double inequality Mλ(a,b) 0 with a ≠ b? Where Mp(a, b) is the pth power mean of two positive numbers a and b.

Suggested Citation

  • Yong-Min Li & Bo-Yong Long & Yu-Ming Chu, 2012. "A Best Possible Double Inequality for Power Mean," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:379785
    DOI: 10.1155/2012/379785
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/379785
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/379785?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Yu-Ming Chu & Shan-Shan Wang & Cheng Zong, 2011. "Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Yu-Ming Chu & Shan-Shan Wang & Cheng Zong, 2011. "Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-9, July.
    3. Yu-Ming Chu & Ye-Fang Qiu & Miao-Kun Wang, 2010. "Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-12, September.
    4. Wei-Feng Xia & Yu-Ming Chu & Gen-Di Wang, 2010. "The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    5. Ming-yu Shi & Yu-ming Chu & Yue-ping Jiang, 2009. "Optimal Inequalities among Various Means of Two Arguments," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    6. Yu-Ming Chu & Ye-Fang Qiu & Miao-Kun Wang, 2010. "Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    7. Ming-yu Shi & Yu-ming Chu & Yue-ping Jiang, 2009. "Optimal Inequalities among Various Means of Two Arguments," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-10, November.
    8. Wei-Feng Xia & Yu-Ming Chu & Gen-Di Wang, 2010. "The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-9, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yong-Min Li & Bo-Yong Long & Yu-Ming Chu & Wei-Ming Gong, 2012. "Optimal Inequalities for Power Means," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Wei-Mao Qian & Bo-Yong Long, 2012. "Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Hongya Gao & Jianling Guo & Wanguo Yu, 2011. "Sharp Bounds for Power Mean in Terms of Generalized Heronian Mean," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    4. Wei-Mao Qian & Zhong-Hua Shen, 2012. "Inequalities between Power Means and Convex Combinations of the Harmonic and Logarithmic Means," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. Yu-Ming Chu & Ye-Fang Qiu & Miao-Kun Wang, 2010. "Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    6. 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).
    7. Ladislav Matejíčka, 2013. "Sharp Bounds for the Weighted Geometric Mean of the First Seiffert and Logarithmic Means in terms of Weighted Generalized Heronian Mean," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    8. Yu-Ming Chu & Miao-Kun Wang & Zi-Kui Wang, 2011. "An Optimal Double Inequality between Seiffert and Geometric Means," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    9. Wei-Feng Xia & Yu-Ming Chu & Gen-Di Wang, 2010. "The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    10. Yang, Zhen-Hang & Chu, Yu-Ming & Zhang, Xiao-Hui, 2015. "Sharp Cusa type inequalities with two parameters and their applications," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1177-1198.
    11. Wei-Ming Gong & Ying-Qing Song & Miao-Kun Wang & Yu-Ming Chu, 2012. "A Sharp Double Inequality between Seiffert, Arithmetic, and Geometric Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    12. 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).
    13. Yu-Ming Chu & Shan-Shan Wang & Cheng Zong, 2011. "Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:379785. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.