Weighted pseudo almost periodic functions and applications to evolution equations with delay

In this paper, we introduce a new class of vector-valued weighted pseudo almost periodic functions and present some basic properties about these new functions. Moreover, we obtain an new existence theorem of vector-valued weighted pseudo almost periodic solution to the evolution equations x′(t)=Ax(t)+f(t,xt)x′(t)=Ax(t)+f(t,xt) with delay in a Banach space X.