$(a+b)^p\leq(1+\epsilon)a^p+C_{\epsilon}b^p$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$
65297
Proof that for $a,b,c\in \mathbb{R}$, hold that $\left |\sqrt {a^2+b^2}-\sqrt {a^2+c^2} \right |\leq \left |b-c \right |$.
26741
How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
61939
Induction of inequality involving AP
144693
Show that if $B \subseteq C$, then $\mathcal{P}(B) \subseteq \mathcal{P}(C)$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
145884
Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$
77493
Classic $c_r$-inequality in $l_r$ space: $E(|X+Y|^r)\leq c_r[E(|X|^r)+E(|Y|^r)]$
141525
Cyclic Inequality $\frac{a^3}{(a+b)(a+c)}$
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
156669
Trying to prove a simple (?) inequality
104922
Inequality $\frac1a + \frac1b + \frac1c \leq \frac{a^8+b^8+c^8}{a^3b^3c^3}$
66261
Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$
81818
Prove or disprove : $\det(A^k + B^k) \geq 0$
72081
$\forall x,y>0, x^x+y^y \geq x^y + y^x$