Proving $||x||-||y|| \leq ||x-y||$
1316
Reverse Triangle Inequality in vector space
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
152311
Proving expression$\geq 2$, where variables are $x,y,z$
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
103536
How to prove $|e^{i\theta} - 1| \leq |\theta|$?
42976
How do you prove the follwing $|\sqrt[n]{x}-\sqrt[n]{y}| \le \sqrt[n]{|x-y|}$
122944
Prove $|y''(x)| \leq 40$ for all $x \in [1,3]$.
76689
How to prove $C_1 \|x\|_\infty \leq \|x\| \leq C_2 \|x\|_\infty$?
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
87567
How to prove $1+x \leq e^x~\forall x \in \mathbb{R}?$
20626
Prove that $x^y < y^x$
126632
Proving Inequalities with Absolute values
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
98921
Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?