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arXiv · 2410.07831

A functional equation for monomial functions

Eszter Gselmann·Mehak Iqbal
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Abstract

Let $\mathbb{F}\subset \mathbb{K}$ be fields with characteristic zero, $n$ be a positive integer and $κ\in \mathbb{K}$. In this paper, we determine those monomials $f\colon \mathbb{F}\to \mathbb{K}$ of degree $n$ for which \[ f(x^{2})= κ\cdot x^{n}f(x) \] holds for all $x\in \mathbb{F}$. 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.

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Eszter Gselmann, Mehak Iqbal. 2024-10-10. A functional equation for monomial functions. https://arxiv.org/abs/2410.07831

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