Estimations of power difference mean by Heron mean (The research of geometric structures in quantum information based on Operator Theory and related topics)

HANDLE Web Site Open Access

Bibliographic Information

Other Title
  • Estimations of power difference mean by Heron mean

Search this article

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

  • RIMS Kokyuroku

    RIMS Kokyuroku 2033 9-21, 2017-06

    京都大学数理解析研究所

Related Projects

See more

Details 詳細情報について

Report a problem

Back to top