Mathematics – Classical Analysis and ODEs
Scientific paper
2012-03-14
Mathematics
Classical Analysis and ODEs
12 pages, submitted to a Journal
Scientific paper
We study discontinuous solutions of the monomial equation
$\frac{1}{n!}\Delta_h^nf(x)=f(h)$. In particular, we characterize the closure
of their graph, $\bar{G(f)}^{\mathbb{R}^2}$, and we use the properties of these
functions to present a new proof of the Darboux type theorem for polynomials
and of Hamel's theorem for additive functions.
Abu-Helaiel Kh. F.
Almira J. M.
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