2024/10/10 by Eszter Gselmann, Gselmann, Eszter, Mehak Iqbal +1
Mathematics · Engineering · #Functional Equations Stability Results #Process Optimization and Integration
paper · pdf · doi:10.48550/arxiv.2410.07831
Let \mathbbF⊂ \mathbbK be fields with characteristic zero, n be a positive integer and κ∈ \mathbbK. In this paper, we determine those monomials f\colon \mathbbF→ \mathbbK of degree n for which f(x2)= κ⋅ xnf(x) holds for all x∈ \mathbbF. We show that similar to the classical results, where additive functions were considered, the monomial functions in the equation can be represented with the aid of homomorphisms and higher-order derivations.