Hello

I'm trying to solve a fixed point problem x=F(x), where F: R^n -> R^n, and would want to show that F is contraction so that the fixed point is unique.

I have seen people using a result which roughly says that if the Jacobian matrix J of F has dominant diagonal, then F is a contraction. Can someone point me to any book/article which has a formal statement and proof of this claim? My statement here may be a little off, and that's why I'm looking for a formal statement/proof to make sure that this is a result that I can use.

I know this result is related to another result that if the spectral radius of J is less than 1, then F is a contraction, if that helps. Thanks.