Lipschitz Property of Norms: Comparing α-norm and β-norm in ℝn

[ovidiupetre]

Homework Statement

Hello friends,

i couldn't find a solution for the question below. Can you help me?

Thank you very much.

Let α-norm and β-norm be two different norms on ℝⁿ. Show that f:ℝⁿ->ℝ^m is Lipschitz in α-norm if and only if it is Lipschitz in β-norm

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

You did read the rules for this forum didn't you? And so you know you are required to show your own attempt to solve it?