I am looking for a proof that this inequality: $$(W_1+W_2+\cdots+W_n)^a \leq W_1^a +\cdots + W_n^a$$ is valid.
I have a power function $f(W)=W^a$ where $a$ is a real number, constant but usually $0\lt a\lt 1$. The $W_i$ are real positive numbers.
Then I want to check if $\left(\sum W_i\right)^a \leq \sum(W_i^a)$
For example for $n=2$ : $(x+y)^a \leq x^a + y^a$.