Hi rdejoy2011,
Welcome to Apple Support Communities. I understand that you're unable to send invites in the Calendar app or that the recipients are not receiving them. I'll be happy to help.
If you haven't tried yet, I recommend testing on both Wi-Fi and cellular data to see if you're able to send invites in the Calendar app. This can help isolate the behavior you're experiencing. In addition, there's specific servers that provides the ability to send and receive invites. For example, iCloud, Microsoft Exchange, and some CalDAV servers let you send and receive meeting invitations. (Not all calendar servers support every feature.) Here's a helpful article with that information, along with the appropriate steps on how to send and receive invitations in the Calendar app: Send and receive invitations in Calendar on iPhone
In addition, if this is an issue you're experiencing with iCloud, I suggest following the steps outlined here: If your iCloud Contacts, Calendars, or Reminders won’t sync Even though this is an article about syncing, these steps are still relevant to the issue you're experiencing and can help.
Kind regards.