The Jacobian Conjecture in case of "non-negative coefficients"

It is known that it is sufficient to consider in the Jacobian Conjecture only polynomial mappings of the form ${\displaystyle F(x₁,...,x_n)=x-H\left(x\right):=(x₁-H₁(x₁,...,x_n),...,x_n-H_n(x₁,...,x_n))}$, where ${\displaystyle H_j}$ are homogeneous polynomials of degree 3 with real coefficients (or ${\displaystyle H_j=0}$), j = 1,...,n and H'(x) is a nilpotent matrix for each ${\displaystyle x=(x₁,...,x_n)\in {ℝ}^n}$. We give another proof of Yu's theorem that in the case of non-negative coefficients of H the mapping F is a polynomial automorphism, and we moreover prove that in that case ${\displaystyle deg{F}^{-1}\le {\left(degF\right)}^{\in dF-1}}$, where ${\displaystyle \in dF:=max\{\in dH\prime \left(x\right):x\in {ℝ}^n\}}$. Note that the above inequality is not true when the coefficients of H are arbitrary real numbers; cf. [E3].