Classifying functions that satisfy $|f(x)-f(y)| \leq M|x-y|^{\alpha}$
80939
How to show that every $\alpha$-Hölder function, with $\alpha>1$, is constant?
39090
Finding functions such that $f(g(x)) = f(x)g(x)$
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
127887
Existence of a meromorphic functions $f(z)$ such that $|f(z)|\geq |z|$.
75882
Countability of local maxima on continuous real-valued functions
2142
Finding a set of continuous functions with a certain property 2
126698
measurability of a function -equivalent conditions
17310
Can $f(x)=|x|^3$ be differentiated
76147
Bounding holomorphic function at 0 given other bounds
6636
Is there a positive function $f$ on real line such that $f(x)f(y)\le|x-y|, \forall x\in \mathbb Q , \forall y \in \mathbb R \setminus \mathbb Q$?
3801
Functions that take rationals to rationals
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
71857
Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
34223
Prove that every function that verifies $|f(x)-f(y)|\leq(x-y)^2$ for all $x,y$ is constant.
64836
Functions that are always less than their derivatives