Pseudo-almost automorphic mild solutions to semilinear integral equations in a Banach space

In this paper, we consider the existence of pseudo-almost automorphic solutions of the semilinear integral equation x(t)=∫−∞ta(t−s)[Ax(s)+f(s,x(s))]ds,t∈R in a Banach space XX, where a∈L1(R+)a∈L1(R+), AA is the generator of an integral resolvent family of linear bounded operators defined on the Banach space XX, and f:R×X→Xf:R×X→X is a pseudo-almost automorphic function. The main results are proved by using integral resolvent families combined with the theory of fixed points.