Proof of a claim on a continuous function in [0,1]
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
28289
Show that $Kf(x,y)=\int_0^1k(x,y) f(y) \,dy\\$ is linear and continuous
30455
Show that any continuous $f:[0,1] \rightarrow [0,1]$ has a fixed point $\zeta$
23436
$f$ Holder continuous with Holder exponent $p>1\implies f \text{ is constant}$
87239
Prove functions defined by sup and inf are continuous
21301
If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$
104510
For continuous $f$, $\int_0^x f(t)dt = ∫_x^1f(t)dt$ implies $f=0$.
13257
How to prove this problem about uniform continuity
55268
Differentiable and Continuous functions on [0,1] with 'weird' conditions.
94781
Prove that $M(t)=\sup_ {a \leq x \leq t} f(x)$ given $f(x)$ is continuous on $[a,b]$
130023
Prove that the sum of two continuous functions is continuous
76607
Show that exists a continuous function in $E$ that is not bounded
150554
proof that $f'$ is continuous at $a$
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
82280
Problem about continuous functions and the intermediate value theorem
126212
Proving uniform continuity on an interval
82405
For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $