(Problem Solving) Proving $|x|^p +|y|^p \geq |x+y|^p$
56391
Is this inequality true? $ (x + y)^{\alpha} < x^{\alpha} + y^{\alpha} $, for positive $x$ & $y$, and for $0 < \alpha < 1$
82591
Prove $(x+r_1) \cdots (x+r_n) \geq (x+(r_1 \cdots r_n)^{1/n})^{n}$.
41300
Show $(x+y)^a > x^a + y^a$ for $x,y>0$ and $a>1$
142785
How can I prove Holder inequality for $0<p<1$?
94119
Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
5765
Show that $[2x]+[2y] \geq [x]+[y]+[x+y]$
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
96153
$ x^3<y^3 \iff x<y $ proof issue.
41364
How to prove that $x^y - y^x = x + y$ has only one solution in positive integers?
148790
Basic question about proofs with the goal $\exists x P(x)$
102464
Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
83752
If $p + q = 1$ prove that for any natural $n, m$ following is true: $(1 - p^n)^m + (1 - q^m)^n \ge 1$
3820
Prove that $||x|-|y||\le |x-y|$
20626
Prove that $x^y < y^x$
147785
Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
149889
Prove that $|\log(1 + x^2) - \log(1 + y^2)| \le |x-y|$