I don’t know the name of a function that would do just that – but i can give you what i think is a good algorithm to do so
However, I suggest you do the following trick :
Once the user publishes new content – let it have a category called “user submission” for example or any other stuff
Once an admin views the post, he can remove that category and label the content accordingly.
So all you have to do is use feedburner or any email notification system to let the people you want know about the “new posts” or RSS subscription by category
to do by programming :
1 – you have to fetch the user details for which users are admins from the tables users/usermeta
2 – in some separate table, you must have lastPostId, AdminId
3 – write a script get the posts that have an ID > lastPostId and send the email
4 – this script can be run using a cron job
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