I'm not sure you can (or should) delete "documents" from a user's inbox. This is like accessing everybody's e-mail inbox and deleting their requirements. Users can select multiple items and delete them from their inbox.
As far as whether you can delete "only" unread document; I don't think that's an issue. If you can find a way to delete any document from a user's inbox then finding out whether it is read or unread shouldn't be difficult. It must be an entry in a table somewhere.