Fixed point theorems for nonexpansive operators with dissipative perturbations in cones

Let P be a cone in a Hilbert space H, A : P → 2 be an accretive mapping (equivalently, −A be a dissipative mapping) and T : P → P be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type −A+T are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in L(Ω).