Does $c\cdot f(x) = f(cx) \implies f$ is linear?
113572
Are all multiplicative functions additive?
152379
If $V_1, V_2$ are $\mathbb{Q}$-vector spaces and $f \colon V_1 \to V_2$ is additive, then $f$ is $\mathbb{Q}$-linear
72006
Suppose $f(x)$ is linear i.e. $f(x + y) = f(x) +f(y) $ and monotone on $[-\infty, +\infty]$, then $f(x) = ax$, a real.
108156
Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
36379
Suppose that $ f $ is entire and that for each $ z $, either $ |f(z)| \leq 1 $ or $ |f^\prime (z) |\leq 1 $. Prove that $ f $ is a linear polynomial.
95340
Locally bounded additive function is linear
22303
How do I prove that $f(x)f(y)=f(x+y)$ implies that $f(x)=e^{cx}$, assuming f is continuous and not zero?
93910
Equality in Cauchy-Schwarz Inequality implies linear dependence.
107248
Prove that the set $ \{\sin(x),\cos(x),\sin(2x),\cos(2x)\}$ is linearly independent.
83461
Continuous iff composition with every linear functional is continuous
47810
$C(X)$ is separable when $X$ is compact?
45676
Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$.
75855
Show that $\det{(A + sxy^*)}$ is linear in $s$
81229
Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
135577
Prove the existence of $c$ such that $f'(c) = 2c(f(c) - f(0))$
24900
Homogeneity and Differentiability at $0$ implies linearity?
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?