Proving $b^a(1-b)^{1-a} \leq a^a(1-a)^{1-a}$ where $0 \leq b \leq a \leq 1$
66247
Proving inequality $\left( \frac {x} {y}\right) ^{x}\left( \frac {1-x} {1-y}\right) ^{1-x}\geqslant 1$
64955
Show that there are $ a,b \geq 0 $ so that $ |f(x)| \leq ax+b, \forall x \geq 0.$
52204
Proof of one inequality $a+b+c\leq\frac{a^3}{bc}+\frac{b^3}{ca}+\frac{c^3}{ab}$
54380
Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$
41300
Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
138036
Proving Inequality using Induction $a^n-b^n \leq na^{n-1}(a-b)$
39082
Proving $x^\alpha-\alpha x \le 1- \alpha $
149287
Prove that $A,B>0$ and $A_{ij}0$
38448
Show that a simple inequality holds: $a<b$ implies $\frac ab < \frac{a+1}{b+1}$
111515
Proving that $-a=(-1)\cdot a$
78736
Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
12954
Prove if $ac>bc$ and $c>0$, then $a>b$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
96133
Prove that $ m_{a} \geq m_{g} \geq m_{h} $ using strict inequalities unless $ a = b $.
25870
Prove that $0 \leq ab + ac + bc - abc \leq 2.$
126032
Proving a certain inequality