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

中文翻译：

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三明治结果的周期性和共轭性

令 P 为\（\ mathcal {M} \）集的非恒定自映射。证明了在自反Banach空间中具有值的\（\ mathcal {M} \）上定义的广义次 P 周期函数的三明治型定理 。特别地，给定函数\（f，g：\ mathcal {M} \ rightarrow \ mathbb {R} \），我们获得了存在广义 P 周期函数\（F：\ mathcal {M } \ rightarrow \ mathbb {R} \）这样\（f \ le F \ le g \）。给出了 F 的公式， 并讨论了其Lipschitz常数。此外，借助新的三明治方法，考虑了功能方程\（f \ circ p = r \ circ f \）的可解性。