Let be X,Y

Banach spaces, f:X -> Y.

f is (locally)

**Lipschitz continuous** at x in X

iff it satisfies the

Lipschitz condition at x.

(There exists M > 0, M of

**R** and an

neighborhood U(x) of x with for all y of U(x) holds ||f(y)-f(x)|| < M ||x - y|| )

f is called Lipschitz continuous if it is Lipschitz continuous for all x of X.

Lipschitz continuous implies continuous.

Continuous differentiable implies Lipschitz continuous.