This is not possible since you don't control the server's that Gmail and Facebook are hosted on.
HOWEVER... there is something you can do to prevent accessing your accounts from cookies, etc.
- The easiest way to prevent access to browsers with possible access is to change your password. Once the password is changed, any attempt to view your logged in Gmail or Facebook account will redirect the viewer to the login page.
- You can turn on 2-step verification this will enable you to protect your account from any access (with valid cookies/password) because a new browser will require an authentication code that is sent to a cell phone number that you provide.
- Also, at the bottom of that page is a link to
Require a verification code the next time I log in from any other computer
- Go to your Account Security Settings and look at the
Active Sessions area. You can end the activity on each of those (you'll have to log in again) but that will require a login from each of the other machines you've access Facebook on.
- Also from that same page you can enable
Login Notifications and
Login Approvals for added security.
I would suggest, however, that you use the
BOTH option that I gave originally. Good luck!