$(x+y)^a \geq x^a + y^a$
49783
A possible inequality related to binomial theorem (or, convex/concave functions)
5465
This inequality $a+b^2+c^3+d^4\ge \frac{1}{a}+\frac{1}{b^2}+\frac{1}{c^3}+\frac{1}{d^4}$
8207
Can I prove this inequality algebraically?
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
149700
Prove that $\frac{a_1^2}{a_1+a_2}+\frac{a_2^2}{a_2+a_3}+ \cdots \frac{a_n^2}{a_n+a_1} \geq \frac12$
23264
Inequality $ \vert \sqrt{a}-\sqrt{b} \vert \leq \sqrt{ \vert a -b \vert } $
110790
Prove the following summation inequality: $\sum_{i=1}^n(a_i)\sum_{i=1}^n(\frac{1}{a_i})\ge n^2$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
7775
Show that $|x-y|\leq |x|+|y|$.
78144
How to prove the inequality $a_1^{a_1}a_2^{a_2}\cdots a_n^{a_n} > \left(\frac{a_1+\dots+a_n}{n}\right)^{a_1+\dots+a_n}$?
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
18477
$(W_1+W_2+\cdots+W_n)^a \leq W_1^a +\cdots + W_n^a$ for $n$ integer, $n\geq 2$, $W\gt 0$ and $a$ constant, real, $0\lt a\lt 1$
68986
Use the triangle inequality to show that $|a|+|b| \leq |a+b|+|a-b|$
29679
Prove: $|x-y|\leq |x|+|y|$
1305
Proving the AM-GM inequality for 2 numbers $\sqrt{xy}\le\frac{x+y}2$
5765
Show that $[2x]+[2y] \geq [x]+[y]+[x+y]$