Monday, June 24, 2019

functional equations - Let $f$ a continuous function defined on $mathbb R$ such that $forall x,y

Let $f$ a continuous function defined on $\mathbb R$ such that $\forall x,y \in \mathbb R :f(x+y)=f(x)+f(y)$




Prove that :
$$\exists a\in \mathbb R , \forall x \in \mathbb R, f(x)=ax$$

No comments:

Post a Comment

analysis - Injection, making bijection

I have injection $f \colon A \rightarrow B$ and I want to get bijection. Can I just resting codomain to $f(A)$? I know that every function i...