Show that $f_1,...,f_n$ are constant if $|f_1|+...+|f_n|$ assumes a local maximum.
5440
Maximum of sum of finite modulus of analytic function.
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$
91352
If $\Re(f)$ is bounded then f is constant.
80939
How to show that every $\alpha$-Hölder function, with $\alpha>1$, is constant?
129343
What is the maximum value of $|f(z)|$ on the unit disc $D=\{z \in \mathbb C:|z|\leq 1\}$?
95340
Locally bounded additive function is linear
131444
Local maximum implies derivative is $0$
57639
Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
72856
Show $f$ is constant if $|f(x)-f(y)|\leq (x-y)^2$.
158407
derivative bounded by a constant multiple of the function
75882
Countability of local maxima on continuous real-valued functions
144745
Proof of: If $x_0\in \mathbb R^n$ is a point of local minimum of $f$, then $\nabla f(x_0) = 0$.
51934
Let $f$ be entire and suppose that $\text{Im} f\ge0$. Show that $\text{Im} f$ is constant.
3818
Proving two entire functions are constant.
60520
Upper bound for $|f(0)|$ based on its behavior within the unit disk.
18950
Show that $f$ has at most one fixed point
64650
If $a\operatorname{Re}(f(z))+b\operatorname{Im}(f(z))=c$ then f is constant