Comparison of two regulatory results on functional equations with few parameters |
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Authors: | Istv��n Kov��csv?lgyi |
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Institution: | 1. Department of Computer Algebra, E?tv?s L??r??nd University, P??zm??ny P??ter s??t??ny 1/c., 1117, Budapest, Hungary
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Abstract: | Two methods to prove regularity properties of the linear functional equation $$f(x)=h_0(x,y)+\sum_{j=1}^n h_j(x,y)f(x+g_j(y)), $$ where ${(x,y) \in D \subset \mathbb{R}^r \times \mathbb{R}^s}$ , ${x \in \mathbb{R}^r}$ and ${y \in \mathbb{R}^s}$ , with few parameters i.e. allowing 1 ?? s < r are examined. It is proved that??under certain conditions, for some class of equations and in some sense??they are equivalent. |
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