Find all functions $f:(0,\infty)\rightarrow(0,\infty)$ subject to the conditions:
133646
real analysis -functional equation
11879
If $\lim_{n\rightarrow\infty} f(n+1) - f(n) = L$, prove that $\lim_{n\rightarrow\infty} f(n)/n = L$
132093
Solve $f(f(x))=f(x)$
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
86409
Show that $\lim_{x \to +\infty}\left(f(x)+f'(x)\right)=0 \Rightarrow \lim_{x \to +\infty} f(x)=0$
153510
Questions about the existence of a function
110704
Find all functions $f$ such that $f(x)+f(\frac{1}{1-x})=x$
43703
Find $\lim _{x\to \infty }\left(x\left(\ln\left(x+1\right)-\ln x\right)\right) $
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
48891
Show that: lim$_{n\rightarrow \infty}\,f(x_n)=f(\text{lim}_{n \rightarrow \infty} \, x_n)$
63889
Prove that if $u_n\rightarrow \infty$ then $\frac{1}{u_n} \rightarrow 0$
107237
Evaluate $\lim_{n\rightarrow\infty} \int_0^1 f(x^n) dx$
82371
$f$ is an entire function with Im $f\geq 0$
77331
$f$ function with $\nabla f=\bar{0}$