LAUSR

Let P be a nonconstant selfmap of a set $$\mathcal {M}$$ M . A sandwich-type theorem for generalized sub- P -periodic functions defined on $$\mathcal {M}$$ M with values in a reflexive Banach space is proved. In particular, given functions $$f,g:\mathcal {M}\rightarrow \mathbb {R}$$ f , g : M → R , we obtain necessary and sufficient conditions for the existence of a generalized P -periodic function $$F:\mathcal {M}\rightarrow \mathbb {R}$$ F : M → R such that $$f\le F\le g$$ f ≤ F ≤ g . The formula for F is given and its Lipschitz constant is discussed. Moreover the solvability of the functional equation $$f\circ p= r\circ f$$ f ∘ p = r ∘ f with the help of a new sandwich method, is considered.