Its easy question, but I cannot find the name of the inequality. Please provide me with it.
I am doing the following, let $a$ be $n$-dimentional vector. Let $b_i, i=1, \ldots, n$ be positive numbers. Then, $$ \left(\left|\sum_{i=1}^n a_i\right|^p\right)^{1/p}=\left(\left|\sum_{i=1}^n(a_i-b_i)+\sum_{i=1}^nb_i\right|^p\right)^{1/p}\leq \left(\left|\sum_{i=1}^n(a_i-b_i)\right|^p\right)^{1/p}+\left(\left|\sum_{i=1}^nb_i\right|^p\right)^{1/p} $$ Which inequality did I use here?
Thank you.
