Comparison of Differences between Power Means 1

@article{Tian2013ComparisonOD,
  title={Comparison of Differences between Power Means 1},
  author={Chang-An Tian and Guanghua Shi and Fei Zuo},
  journal={International Journal of Mathematical Analysis},
  year={2013},
  volume={7},
  pages={511-515}
}
We show that the differences of power means associated to distinct sequences of weights are comparable, with constants that depend on the smallest and largest quotients of the weights. The obtained results are then utilized to generalize the operator arithmetic-geometric-harmonic mean inequalities. Mathematics Subject Classification: Primary 47B20; Secondary 47A10 

References

SHOWING 1-6 OF 6 REFERENCES
COMPARISON OF DIFFERENCES BETWEEN ARITHMETIC AND GEOMETRIC MEANS
We complement a recent result of S. Furuichi, by showing that the differences $\sum_{i=1}^n \alpha_i x_i - \prod_{i=1}^n x_i^{\alpha_i}$ associated to distinct sequences of weights are comparable,
On refined Young inequalities and reverse inequalities
In this paper, we show refined Young inequalities for two positive operators. Our results refine the ordering relations among the arithmetic mean, the geometric mean and the harmonic mean for two
About the precision in Jensen-Steffensen inequality
The main objective of the present paper is to estimate the precision of Jensen-Steffensen inequality. We obtain results that complement, generalize, unify and agree with some of the previously known
Pečarić, Jensen’s operator and applications to mean inequalities for operators in Hilbert space
  • Bull. Malays. Math. Sci. Soc. 35(2012),
  • 2012
Pečarić, A variant of Jensen’s inequality for convex functions of several variables
  • J. Math. Inequal
  • 2007