Weighted Pseudo Almost Periodic Solutions to a Class of Semilinear Integro-Differential Equations in Banach Spaces

In this paper we prove the existence of weighted pseudo almost periodic mild solutions for the class of integro-differential equations in the form (Formula presented.) is a Stepanov-like weighted pseudo almost periodic function and A generates an immediately norm continuous C0-semigroup on a Banach space X. Also, we give a short proof to show that the vector-valued space of Stepanov-like weighted pseudo almost periodic functions is a Banach space. © 2015, Alvarez and Lizama; licensee Springer.