stationary point of a periodic function.
134043
Prove that for $ f(x+2\cdot\pi)=f(x), x \in \mathbb{R} $, there exists $ x_0 $ so $ f(x_0+\pi)=f(x_0) $
118048
Can a function with just one point in its domain be continuous?
64134
The difference between two periodic functions converges to zero, is this two functions identical?
126259
Minimum of a function on an open interval
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
35133
Every increasing function from a certain set to itself has at least one fixed point
42638
Showing that a function $f$ has a unique fixed point in a metric space.
54729
Prove that $f$ has a fixed point .
33628
Prove that $\sin(\sqrt x)$ not periodic
152701
A question on periodicity of complex functions
105497
A function satisfying a series equation
96495
Periodicity of a Function Given the Functional Equation $f(x+a)=\frac12+\sqrt{f(x)-\big(f(x)\big)^2}$
144957
Uniform convergence of a function
38192
Derivative of inverse function at a point.
18950
Show that $f$ has at most one fixed point
54297
Is $f(x)=10$ a periodic function?
131992
A problem on continuous functions