Hadamard functions preserving nonnegative H-matrices (Q1307578)

This paper classifies all continuous Hadamard functions that preserve the nonnegative H-matrices. It is known that the Hadamard functions \(f(x_1,...,x_n) = cx_1^{\alpha_1} \cdots x_k^{\alpha_k}\) satisfy two functional inequations for nonnegative H-matrices. Thus these functions preserve them. Here it is shown that the only continuous functions that map the nonnegative H-matrices to themselves are precisely those \(f\).