$(x+y)^c\le x^c+y^c$ for $0<c\le1$
3109
Prove that $(p+q)^m \leq p^m+q^m$
10859
Prove $\sup(f+g) \le \sup f + \sup g$
83386
Inequality with exponents $x^x+y^y \ge x^y +y^x$
124320
$a,b,c>0 \text{ s.t. }a+b+c=1 \implies \sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ca+b} \ge 1+ \sqrt{ab}+\sqrt{bc}+\sqrt{ca}$
72081
$\forall x,y>0, x^x+y^y \geq x^y + y^x$
82612
Show that $\frac c {1+c} \le \frac a {1+a} + \frac b {1+b}$ , for $c \le a+b$ and $a,b,c \ge 0$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
101286
How show that $|a_{n}-1|\le c\lambda ^n,\lambda\in (0,1)$
33332
A classic exponential inequality: $x^y+y^x>1$
121353
If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
56391
Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
116387
How to prove that $\Gamma(x) \leq x^x$ for $x \geq 1$
61859
Prove $\sum \frac{a}{a+b^4+c^4} \le 1$
115176
Can we say that $\left(a+b\right)^{\alpha}>a^{\alpha}+b^{\alpha}$ for all $a,b>0$ and $\alpha>1$?
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.