A Note on Monomials |
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| Authors: | Jose María Almira Khader Faiez Abu-Helaiel |
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| Institution: | 1. Departamento de Matemáticas, Universidad de Jaén. E.P.S. Linares, C/ Alfonso X el Sabio, 28, 23700, Linares (Jaén), Spain
2. Departamento de Estadística e Investigación Operativa, Universidad de Jaén, Campus Las Lagunillas, 23071, Jaén, Spain
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| 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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