Facebook Application

I'm not too familiar with apps, but would be it be possible to create an app for fanpages where the user allows access for the app to control their event invitations and etc?

I know there's no way to invite ppl to events via fanpages, but with an app that the user allows permission to, is it possible? Basically I'm just wondering to what extent and the details of an app that control a user's events.

As previously mentioned, I'm not an app developer nor have I really worked with any more advanced apps like this...

So I'm looking for a more simplified explanation and breakdown of how far you can go with an app of that variety. Thanks.