Prove that $\min_{x,y} f(x,y) = \min_{x}(\min_{y}f(x,y))$
65827
When $\min_{x \in X,y \in Y} f(x,y) = \min_{x \in X} \min_{y \in Y} f(x,y)$?
29679
Prove: $|x-y|\leq |x|+|y|$
115513
Find the minimum of $\sqrt{(x+1)^2+(y-1)^2}+\sqrt{(x+2)^2+(y+2)^2}+\sqrt{(x-1)^2+(y+1)^2}$ For real $x,y$
96382
Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$?
33389
What's the minimum of $\int_0^1 f(x)^2 \: dx$, subject to $\int_0^1 f(x) \: dx = 0, \int_0^1 x f(x) \: dx = 1$?
121264
Prove that rank $(g \circ f)\le \min[\operatorname{rank}(f),\operatorname{rank}(g)]$; $g$ and $f$ are linear mappings
74202
Show that $|f(z_1)|=|f(z_2)|≤|z_1|^2=|z_2|^2$.
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
102764
Let $f(x)=\int_0^1|t-x|t~dt$ for all real $x$. Sketch the graph of $f(x)$, what is the minimum value of $f(x)$
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
43181
What is the joint distribution of $Z=\min(X,Y)$ and $I_{Z=X}$?
141852
Prove that $2\int_a^b \int_a^x f(x)f(y) \, dy \, dx = \left[ \int_a^b f(x) \, dx \right]^2$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
48154
Find the minimum value of $f(x,y,z)=\frac{x^2}{(x+y)(x+z)}+\frac{y^2}{(y+z)(y+x)}+\frac{z^2}{(z+x)(z+y)}$.
116056
Prove that $|f(x)-f(y)|\le|x-y|$ for all $x$ and $y$.
3820
Prove that $||x|-|y||\le |x-y|$