$(x+y)^p\leq x^p+y^p$ for positive x, y and 0<p<1
3109
Prove that $(p+q)^m \leq p^m+q^m$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
157733
Are positive real numbers $x,y$ allowed to be taken out during this proof?
35867
Squaring sides of an inequality
7775
Show that $|x-y|\leq |x|+|y|$.
151985
If $p$ is a prime and $x,y \in \mathbb{Z}$, then $(x+y)^p \equiv x^p+y^p \pmod{p}$
64239
Upper Bound for $p(1-p) $ where $0 \le p \le 1$
128558
Inequality between $\ell^p$-norms
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
79773
What is $P(X > 0 \mid X + Y > 0)$ given that $X, Y$ are i.i.d standard normal?
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
59513
For $a, b \geq 0$, $0 < x < 1$, show $(a+b)^x \leq a^x + b^x$
28822
$|x| - |y| \leq |x-y|?$
98921
Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
156555
Inequality $\sqrt{1+x^2}+\sqrt{1+y^2}+\sqrt{1+z^2} \le \sqrt{2}(x+y+z)$
125817
show this inequality $(x+y)^3+(y+z)^3+(z+w)^3+(w+x)^3\ge 8(x^2y+y^2z+z^2w+w^2x)$