Abstract
We study discontinuous solutions of the monomial equation \({{\frac{1}{n!} \Delta _{h}^{n}f(x) = f(h)}}\) . In particular, we characterize the closure of their graph, \({\overline{G(f)}^{\mathbb{R}^{2}}}\) , 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.
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