On the sum of squared logarithms inequality and related inequalities

@article{Dannan2014OnTS,
  title={On the sum of squared logarithms inequality and related inequalities},
  author={Fozi M. Dannan and Patrizio Neff and Christian Thiel},
  journal={arXiv: Classical Analysis and ODEs},
  year={2014}
}
We consider the sum of squared logarithms inequality and investigate possible connections with the theory of majorization. We also discuss alternative sufficient conditions on two sets of vectors $a,b\in\mathbb{R}_+^n$ so that $\sum_{i=1}^n(\log a_i)^2\ \leq\ \sum_{i=1}^n(\log b_i)^2\,.\notag $ Generalizations of some inequalities from information theory are obtained, including a generalized information inequality and a generalized log sum inequality, which states for $a,b\in\mathbb{R}_+^n$ and… 
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19 References

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