Accretive equations in cones of Banach space

The purpose of this paper is to study the existence of solutions for the equation x′(t) = −Ax(t), x(0) = x D(A), where P is a cone of a Banach space and A : P → P is an accretive mapping satisfying (I + λA)(P) = P, and to give some sufficient conditions which ensure A(D(A)) = P and (I + λA)(D(A)) = P.