Eigenvalue location of certain matrix polynomials

It is known that a matrix polynomial with unitary matrix coefficients has its eigenvalues in the annular region $\frac{1}{2}<\mathrm{\mid }\lambda \mathrm{\mid }<2$. We prove in this short note that under certain assumptions, matrix polynomials with either doubly stochastic matrix coefficients or Schur stable matrix coefficients also have eigenvalues in similar annular regions.