Outlook notifications do not work on iphone

Go to Settings and tap Notifications. Select an app under Notification Style. Under Alerts, choose the alert style that you want. If you turn on Allow Notifications, choose when you want the notifications delivered — immediately or in the scheduled notification summary.

Use notifications on your iPhone, iPad, and iPod touch

1. Id this your corporate outlook email account? Then please contact the system administrator of your corporate
2. Is this your corporate iPhone? Then please contact the system administrator of your corporate
3. If it is your personal device, in that case, do you have any profile installed by your corporate/organisation/enterprise/School Management?
   1. Erase the profile added by you If you have installed a profile on your own --> Install or remove configuration profiles on iPhone - Apple ...
   2. Or please contact the system administrator of the organisation who provided the profile to you

Have you enabled Scheduled Summary?

Settings > Notifications > [Select the App that you are having trouble receiving immediate notifications]

See the pic below for a few examples. Please select immediate delivery.

Gary Davison wrote:

I am wondering is this something that Apple needs to address also.

Apple Support Community Forum

This is Apple Support Community forum, for user-to-user interaction for information & idea sharing between users, if need be, extend support on technical know-how in handling Apple products from a more experienced fellow users, Apple Inc is neither here nor they are listening. 

Apple Inc says; "We read all feedback carefully, but please note that we cannot respond to the comments you submit."

Feedback - Apple.com Website - Apple

Are you referring to the Outlook app or Outlook on iOS mail app is not clear to me from your post.