How do I turn off the notification on the lower left corner? I tried to turn off notifications in Settings for the app, but it didn't work. iOS 9.0.2.
Those are not notifications, those are apps that are suggested by iOS due to location and usage, or by Handoff from your other devices.
To change the settings for those, change the toggles in
General > Handoff & Suggested Apps in the
Settings app. Toggle everything off if you do not use Handoff and do not want to see any suggestions.