Using the Mazur–Orlicz theorem and some results about the Fréchet functional equation, we consider functional equations related to generalized monomials of degree n. From these considerations, we give some results on existence of single-valuedness and selections for convex-valued maps satisfying functional inclusions. Also, the Diaz–Margolis fixed point alternative is applied to solve the stability problem for set-valued generalized monomials of degree n. Finally, several particular cases are discussed and some applications are given.

中文翻译：

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凸值G-m-代名词及其在稳定性理论中的应用

利用Mazur-Orlicz定理和有关Fréchet泛函的一些结果，我们考虑与n次广义单项式有关的泛函。基于这些考虑，我们给出了关于单值性的存在和满足功能包含的凸值映射选择的一些结果。同样，采用Diaz-Margolis不动点替代方法来解决阶数为n的集值广义单项式的稳定性问题。最后，讨论了几种特殊情况，并给出了一些应用。