I want an inequality of the form : $\Vert a - b \Vert^2 \leq k.(\Vert a\Vert^2 + \Vert b\Vert^2)$ ? where k is a constant.
The norm in consideration is the euclidean norm, and $a$ and $b$ are vectors in $\mathbb{R} ^p$.
As a few people have replied below, its pretty straightforward with k = 2. But I was wondering if there is something tighter than that? Clearly k = 1 if a and b are independent (if random) or orthogonal.