Suppose you have this two Lipschitz continuous functions:
$f_1$ ,with constant $L_1$ and $f_2$ with constant $L_2$.
I have to prove that $f_2 - f_1$ is Lipschitz continuous with constant $L_1+L_2$.
I did like this:
By the triangle inequality:
But I´m having problems in this last line,above...I should have $|y-x|$ in both,isn´t it?What´s wrong?how to proceed?Thanks?