Is there any method to send private message to my application’s users on Facebook?
Sometimes Facebook e-mail me about their question from developer (noreply@facebookmail.com), I can send them e-mail, but it is not very efficent (probably they check their facebook account more than their e-mail). So if its possible I want to send them a facebook message too.
No – this is not possible. It would open up a huge vulnerability for spam. (not that your application is spammy – just saying 😉 )
You could however use App Generated Requests to interact with your users when they are not connected to your application. App generated requests are identical to normal requests that users send to each other ( invites to applications for example ). The only difference is that they are initiated by your application and they do not require the user to be using your app at that moment in time. One limitation however is that you can only interact this way with users that have already authenticated with your application.