On quasimonotone increasing homeomorphisms

Let f is an element of C(R-n, R-n) be quasimonotone increasing such that Ps i (f(y) - f(x)) less than or equal to - c Psi (y - x) (x much less than y) for a linear and strictly positive functional Psi and c > 0. We prove that f is a homeomorphism with decreasing and Lipschitz continuous inverse and w e prove the global asymptotic stability of the equilibrium solution of x' = f(x).