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In this paper, we establish a new composition theorem for \(S^p\)-weighted pseudo almost periodic functions under weaker conditions than the Lipschitz ones currently encountered in the literatures. We apply this new composition theorem along with the Schauder's fixed point theorem to obtain new existence theorems for weighted pseudo almost periodic mild solutions to a semilinear differential equation in a Banach space

A new composition theorem for $S^p$-weighted pseudo almost periodic functions and applications to semilinear differential equations