Ecuatie functionala

[Marius Mainea]

Determinati functiile \( f : (0,\infty)\rightarrow \mathbb{R} \) continue cu proprietatile :

1) \( f(x)=\frac{1}{x}\int_x^{ex}f(t)dt , x>0 \),

2) exista \( \lim _{x\to\infty}xf(x)\in \mathbb{\overline{R}} \).

Nelu Chichirim, Shortlist ONM 2009