On 1-Set-Contraction Perturbations of Accretive Operators in Cones of Banach Spaces

AbstractLetPbe a cone in a Banach spaceE. In this paper, we show the existence of solutions of the operator equationy∈−Ax+Txfory∈P, whereTis a 1-set-contraction operator inPandAis an accretive operator inPsatisfyingR(I+λA)=Pfor all λ>0. Further, a sufficient condition forR(I+λA)=Pis also given