a continuous function, satisfying $f(α) = f(β) +f(α −β)$ for any $α, β ∈ \mathbb{R}$
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
100740
proof of that a continuous function has a fixed point
136594
Proving the existence of a sequence of polynomials convergent to a continuous function $f$.
141938
Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
98772
Continuity of a function in $\mathbb{R}$
14975
Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
17343
Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
141223
$f(x^2) = 2f(x)$ and $f(x)$ continuous
125788
A function with a property $f(x+y)=f(x)f(y)$
143174
property of continuous function
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
102143
$f:\mathbb R\rightarrow \mathbb R$ be a continuous function such that $\int_{0}^{\infty}f(x)dx$ exists.
128911
Continuous extension of a real function
68165
Find a function $f: \mathbb{R} \to \mathbb{R}$ that is continuous at precisely one point?
88240
Two functions discontinuous, but sum continuous
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
93021
$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$