One suggestion I have is to show that since the system is continuous then it belongs to a Banach space and then use the Banach-Norm inequality to justify the condition.
Thanks for your reply, but I'm not familiar with the Banach Norm.
I don't think my prof. would give me a problem that needs to be solved with material he hasn't taught in class. I think the problem needs to be solved with what is given. The problem is that I can't figure how to connect equations 1 and 2.
If you have any more ideas please let me know.