Estimations of power difference mean by Heron mean (The research of geometric structures in quantum information based on Operator Theory and related topics)
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- Ito, Masatoshi
- Maebashi Institute of Technology
Bibliographic Information
- Other Title
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- Estimations of power difference mean by Heron mean
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Abstract
In this report, we discuss estimations of power difference mean by Heron mean. We obtain the greatest value $alpha$=$alpha$(q) and the least value $beta$=$beta$(q) such that the double inequality K_{$alpha$}(a, b)<J_{q}(a, b)<K_{$beta$}(a, b) holds for any a, b>0 and q in mathbb{R}, where J_{q}(a, b)=overline{q}^{mathrm{L}{frac{a^{q+1}-b^{q+1}{a^{mathrm{q}-bmathrm{q}+1 is the power difference mean and K_{q}(a, b)=(1-q)displaystyle sqrt{ab}+qfrac{a+b}{2} is the Heron mean. We also get similar inequalities for bounded linear operators on a Hilbert space.
Journal
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- RIMS Kokyuroku
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RIMS Kokyuroku 2033 9-21, 2017-06
京都大学数理解析研究所
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Details 詳細情報について
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- CRID
- 1050564288162757632
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- NII Article ID
- 120006578993
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- NII Book ID
- AN00061013
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- ISSN
- 18802818
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- HANDLE
- 2433/236766
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- NDL BIB ID
- 028508583
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- Text Lang
- en
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- Article Type
- departmental bulletin paper
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- Data Source
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- IRDB
- NDL
- CiNii Articles