共查询到20条相似文献,搜索用时 93 毫秒
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Jürg Rätz 《Aequationes Mathematicae》2013,86(1-2):187-200
For an abelian group (G, + ,0) we consider the functional equation $$f : G \to G, x + f(y + f(x)) = y + f(x + f(y)) \quad (\forall x, y \in G), \quad\quad\qquad (1)$$ most times together with the condition $$f(0) = 0.\qquad\qquad\qquad\qquad\qquad (0)$$ Our main question is whether a solution of ${(1) \wedge (0)}$ must be additive, i.e., an endomorphism of G. We shall answer this question in the negative (Example 3.14) Rätz (Aequationes Math 81:300, 2011). 相似文献
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Monatshefte für Mathematik - An extension of the linearity of the continuous solutions of the functional equation $$f(x+y)=f(x)+f(y)$$ to measurable functions is presented. 相似文献
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Aequationes mathematicae - 相似文献
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Marcin Balcerowski 《Aequationes Mathematicae》2009,78(3):247-255
We solve the equation
f(x+g(y)) - f(y + g(y)) = f(x) - f(y)f(x+g(y)) - f(y + g(y)) = f(x) - f(y) 相似文献
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Aequationes mathematicae - 相似文献
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We show that the Diophantine system 相似文献
$$\begin{aligned} f(z)=f(x)f(y)=f(u)f(v) \end{aligned}$$ |