For a map between Banach spaces, having this property for a compact subset of the domain implies that the function satisfies the Lipschitz condition on that subset.
For a map between Banach spaces, having this property for a compact subset of the domain implies that the function satisfies the Lipschitz condition on that subset. The Weirstrass function(*) is continuous everwhere but does not have this property anywhere, and in the complex plane, being analytic is equivalent to having the complex version of this property. For ten points, identify this property which a function possesses if the inverse of an integral exists for it.
For a map between Banach spaces, having this property for a compact subset of the domain implies that the function satisfies the Lipschitz condition on that subset.
differentiability (accept word forms, e.g. differentiable)