Constant function with maximum modulus
117595
Minimum Modulus Principle for a constant fuction in a simple closed curve
17406
Determine all the extrema of a function subject to a non-linear constraint.
41847
Uniformly continuous function with unbounded variation
122300
Maximizing a quadratic function subject to $\| x \|_2 \le 1$
93094
How do I solve this problem on maximizing sum modulo a given number?
28011
Does there exists an entire function such that for each $|z|>C$ for some constant $C$, $|f(z)|=|z|+1$?
91398
Continuous function on R which tends to infinity on open interval must have a minimum
62251
"Maximum common divisor" for entire functions
115636
Show that $f$ is either injective or a constant function.
153798
Problem involving maximum and minimum of a continuous function
28120
Are intervally constant analytic functions always constant?
74245
Characterizing non-constant entire functions with modulus $1$ on the unit circle
727
Prove that any continuous integer-valued function of a real variable is constant.
84103
Let $f(z)$ be entire function. Show that if $f(z)$ is real when $|z| = 1$, then $f(z)$ must be a constant function using Maximum Modulus theorem
96050
$f$ an analytic function on $\mathbb{C}$ which takes values in $\mathbb{C}\backslash(-\infty,0]$ implies constant
776
Entire function with positive real part is constant (no Picard)
112211
Show an increasing function f from omega_1 to R is eventually constant