You are using a deprecated method and should switch to using graph api requests.
In this case, you can use the Event object in the graph.
Doing the same thing with the graph api should look something like:
https://graph.facebook.com/EVENT_ID/invited/USER_ID
or
https://graph.facebook.com/EVENT_ID/invited?users=USER_ID1,USER_ID2,USER_ID3
(You should have the create_event permission and an active access token of course)
This is copied from the document, under the invited section. You might also might want to check the attending, maybe and declined sections.
You can use the Graph API Explorer tool to test graph calls.
Edit
I'm sorry for not including this with my original answer:
The invitation made by the graph api (or the deprecated REST) does not result in notifications in the users' side.
You can find a few more threads about this subject here:
But the best indication for this being the case can be found in this bug ticket: Bugs - No Notifications on Event invites via Graph API.
Notice the response from facebook:
event invites do not currently render an on-site notification, this is
a deliberate limitation of the API Event invites made this way will
still increment the counter in the 'events' bookmark and add the event
to the user's events list
Hope this clarify things.