Help Notification Glitch?

[eighteesix]

I receive push email notifications from iCloud and Gmail no problem. However, if I email myself, no notification occurs, if using one service. If my icloud sends a message to my gmail, that shows a notification, however, if I email myself iCloud to iCloud or gmail to gmail, i dont receive a notification at all. Is this normal? How could this be?

issue is with gmail app