I have created several different calendars each for a different person. Upon creating an event in their calendar is it possible to send SMS reminders or notifications to the different mobile devices?
I'm afraid you can't, not with stock Google Calendar.
If you go into settings and look at Mobile Setup, you'll see that you can only define a single phone number to receive SMS alerts.
To accomplish what you want, you'll need to share those calendars with those people and they need to use the Google Calendar app on their phone. From there they can set up their own criteria for getting alerts. (I do something similar with calendars I have shared with my kids.)
(You might be able to do something with Gmail filters auto-forwarding to the email gateway for each person's carrier. But with all of the permissions you need to get in order to forward email automatically and the burden of making sure the calendar alerts will trigger the filters, I think it's hardly worth pursuing.)