| Tartalmi leírás: |
Let $mathbb(F)subset mathbb(K)$ be fields with characteristic zero, $n$ be a positive integer and $kappain mathbb(K)$. In this paper, we determine those monomials $fcolon mathbb(F)to mathbb(K)$ of degree $n$ for which
[
f(x^(2))= kappacdot x^(n)f(x)
]
holds for all $xin mathbb(F)$. 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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