Here is how I stopped email notifications on iPhone 5. I
I turned off notifications in:
- Settings -> Sounds -> New Mail -> Alert Tones -> None.
- Settings -> Notifications -> Mail -> iCloud -> New Mail Sound -> None.
This alone did not work. Then, so I also turned off the iPhone and thensubsequently turned it back on, and it worked.
I don't have G mailGmail, so I didn't address that.