Is it true that $\|(I+A)^{-1}\|_\infty \leq \|(I-B)^{-1}\|_\infty$ if $|A|<B$? What if $A$ and $B$ are triangular matrices?
Definition 1: $|A| = [|a_{ij}|]$, absolute value of every entry of $A$.
Definition 2: $A<B$ if for every entry, $a_{ij}<b_{ij}$.
ANY suggestion is appreciated.