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Results tagged with functional-equations
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user 38620
5
votes
1
answer
336
views
A variant of Cauchy-type functional equation conjecture
Let $f:\mathbb{C}\to \mathbb{C}$ be a complex function such that
$$|f(x-y)|=|f(x)-f(y)|,\qquad x,y\in\mathbb{C}.$$
Is it true that $$f(x+y)=f(x)+f(y),\qquad x,y\in\mathbb{C}?$$
The answer is affirmat …
- 4,280
13
votes
Accepted
A variant of Cauchy-type functional equation conjecture
counterexample
$$f(x)=1-e^{\Re(x) i}$$
- 4,280