You cannot send user messages from your application. If this were possible, we would see many applications sending spam to everyone. You can send application requests to your users when you want to notify them of a change in your application.
You can learn more about application requests and requests at this URL:
https://developers.facebook.com/blog/post/464/
Scroll down to "PHP Example Application-Generated Request" ...
<?php
$app_id = YOUR_APP_ID;
$app_secret = YOUR_APP_SECRET;
$token_url = "https://graph.facebook.com/oauth/access_token?" .
"client_id=" . $app_id .
"&client_secret=" . $app_secret .
"&grant_type=client_credentials";
$app_access_token = file_get_contents($token_url);
$user_id = THE_CURRENT_USER_ID;
$apprequest_url ="https://graph.facebook.com/" .
$user_id .
"/apprequests?message=’INSERT_UT8_STRING_MSG’" .
"&data=’INSERT_STRING_DATA’&" .
$app_access_token . "&method=post";
$result = file_get_contents($apprequest_url);
echo("Request id number: ", $result);
?>
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