My email domain does not exist anymore and certain outgoing emails bounce back for same reason

My email domain does not exist anymore and certain outgoing emails bounce back for same reason

Whenever anyone sends me an email, the email gets bounced back with this message:
 

Delivery has failed to these recipients or groups:

m.e@avcap.net
A problem occurred and this message couldn't be delivered. Check to be sure the e-mail address is correct. If the problem continues, please contact your helpdesk.  

Diagnostic information for administrators:

Generating server: nyexpgp01.shearman.com

m.e@avcap.net
#< #5.4.4 X-PGP-Universal; Host or domain name not found. Name service error for name=avcap.net type=A: Host not found> #SMTP#

 
When I send emails out I get this message:
 
This message was created automatically by mail delivery software.
A message that you sent could not be delivered to one or more of its recipients. This is a permanent error.

SMahajan@canaccordgenuity.com Error, ERROR_CODE :553, ERROR_CODE :5.1.8 Domain of sender address does not exist
  
When I run an SMTP test I get a message saying that the domain avcap.net does not exist.
 
Please help, I am expecting important emails as we speak.