Composition principles for generalized almost periodic functions

In this paper, we consider composition principles for generalized almost periodic functions. We prove several new composition principles for the classes of (asymptotically) Stepanov $p$-almost periodic functions and (asymptotically, equi-)Weyl $p$-almost periodic functions, where $1\le p<\mathrm{\infty },$ and explain how we can use some of them in the qualitative analysis of solutions for certain classes of abstract semilinear Cauchy inclusions in Banach spaces.