Persistent "You got a mail." dialog
That looks like a carrier message, sent by SoftBank.  I will be pushed to your iPhone when somebody sends a message to your SoftBank address.  To turn if off:


  Follow these steps to disable incoming notification for E mail (i): In Home Screen, tap Safari, open Bookmarks and tap My SoftBank and tap @. Enter Login ID and Password (sent via SMS). E mail (i) setting page appears. Tap [3] Newly arriving e-mail notification setting, then tap Off.


See more details here.