Generalization of Weighted Stepanov-Like Pseudo-Almost Automorphic Space

In this paper we introduce and study a new class of functions called weighted Stepanov-like pseudo-almost automorphic functions with variable exponents, which generalizes the class of weighted Stepanov-like pseudo-almost automorphic functions. Basic properties of these new spaces are established. The existence of weighted pseudo-almost automorphic solutions to some first-order differential equations with Sp,q(x)-pseudo-almost automorphic coefficients will also be studied.