If $\textbf{x} \in \mathbb{R}^n$, show that the following inequalities hold.
87582
Some inequalities between 1- norm, 2- norm and infinity-norm: $\|x\|_2\leq\sqrt{\|x\|_1\| x\|_\infty}\leq\frac{1+\sqrt{n}}{2}\|x\|_2$
40930
Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$
7974
lim sup inequality $\limsup ( a_n b_n ) \leq \limsup a_n \limsup b_n $
32149
Proof of the inequality $(x+y)^n\leq 2^{n-1}(x^n+y^n)$
143968
Proving this inequality by mathematical induction
2504
Inequality $\left|\,x_1\,\right|+\left|\,x_2\,\right|+\cdots+\left|\,x_p\,\right|\leq\sqrt{p}\sqrt{x^2_1+x^2_2+\cdots+x^2_p}$
9451
Show bounded and convex function on $\mathbb R$ is constant
118049
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
91740
Hadamard's inequality proof
144382
Proving $\lVert x \rVert_3$ is smaller than euclidean norm
24585
Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
139158
Inequality concerning nonnegative numbers (related to Hanner's inequalities)
91871
Proving quadratic inequalities?
138490
An inequality with a weird condition
67851
Does $|x|^p$ with $0<p<1$ satisfy the triangle inequality on $\mathbb{R}$?
115464
Inequality involving inner product and norm
143067
Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$.