Let f : R ->R be a function.
We say that f is Lipschitz continuous if there is some
L > 0 such that |f(x) − f(y)| < L|x − y| for all x, y in R.
letting f, g : R -> R be lipschitz continious funtions,
(a) i want to show that f+g is lipschitz continious too
and also if f,g are bounded lip continuos funtions
(b) then i want to show that f.g is lipschitz continous too
does anyone know how to show these?