Functional equations stemming from numerical analysis
Tomasz Szostok
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Always when a numerical method gives exact results an interesting functional equation arises. And, since no regularity is assumed, some unexpected solutions may appear. Here we deal with equations constructed in this spirit. The vast majority of this paper is devoted to the equation and its particular cases. We use Sablik’s lemma to prove that all solutions of (1) are polynomial functions. Since a continuous polynomial function is an ordinary polynomial, the crucial problem throughout...