Find the non negative continuous function defined over $[0,1]$ and satisfy given equations
54797
Find the continuous function defined over $[0,1]$ such that $\int_0^1f(x){\rm d}x=1, \int_0^1 xf(x){\rm d}x=a$ and $\int_0^1x^2f(x){\rm d}x=a^2 .$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
33330
Continuous Functions from $\mathbb{R}$ to $\mathbb{Q}$
88240
Two functions discontinuous, but sum continuous
92089
If $f:[a,b]\to \mathbb{R}$ is continuous and nonnegative and $\int_a^b{f}=0$, then $f(x)=0$ for all $x\in [a,b]$
44057
Pointwise but not uniform convergence of continuous functions on $[0,1]$
145368
How to show $f:Y\to X^{+}$ is continuous?
61640
Prove c exists for f:[0,1] -> R
132013
How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
20568
Does the following have a solution for f(x,y)?
95970
Let $f:[0,1] \rightarrow \mathbb{R}$ be a continuous function. If $f(0)=f(1)$ then exists $x\in [0,1]$ s.t. $f(x) = f(x+\frac{1}{2})$
100465
Does there exist a continuous bijection from $(-1,1) \to (-1,1]$?
13224
Continuous function positive at a point is positive in a neighborhood of that point
143174
property of continuous function
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
151410
Inequality of continuous functions
16212
If $f$ is continuous, nonnegative on $[a, b]$, show that $\int_{a}^{b} f(x) d(x) = 0$ iff $f(x) = 0$