Comparison of differences between arithmetic and geometric means

J. M. Aldaz

Comparison of differences between arithmetic and geometric means

Classical Analysis and ODEs 2010-10-08 v2

Authors: J. M. Aldaz

Abstract

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, with constants that depend on the smallest and largest quotients of the weights.

Keywords

inequalities for means

Cite

@article{arxiv.1001.5055,
  title  = {Comparison of differences between arithmetic and geometric means},
  author = {J. M. Aldaz},
  journal= {arXiv preprint arXiv:1001.5055},
  year   = {2010}
}

Comments

Improvements on the bounds after becoming aware of the paper by Sever S. Dragomir, "Bounds for the normalised Jensen functional", Bull. Austral. Math. Soc. 74 (2006), no. 3, 471--478. Correction of an error and of some typos

Comparison of differences between arithmetic and geometric means

Abstract

Keywords

Cite

Comments

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