If there are no MX records for yourmailserver.com the receiving mail server will terminate the connection after the initial HELO command (or delete it after accepting).

If the beginning HELO command argument is not acceptable a 501 failure reply must be returned. If the commands in a transaction are out of order a 503 failure reply must be returned. See: How Email Works
(Command - a request for mail service action sent by the sender SMTP to the receiver SMTP)

If there is one or more MX records associated with the domain yourmailserver.com the receiving mail server then determines if the sending mail server yourmailserver.com is one of those machines listed with MX record. If not, the receiving mail server will not accept mails after the initial handshaking HELO command (or delete it after accepting).

If yourmailserver.com (the sending mail server) is listed as a valid mail server for the domain in question, and a reverse nslookup of the IP address name also associated with that IP address, for example:

The owners of that IP address matches the name of the sending server (yourmailserver.com) only then, will the receiving mail server accept any inbound mails—what it mean is that your mails will be rejected by the recipient mail server if any one of these conditions is not met:

1. Your mail server (ie: yourmailserver.com) do not have a valid name?

2. Your mail server (ie: yourmailserver.com) do not have MX records for the domain?

3. Your mail server (ie: yourmailserver.com) do not matches correctly via a reverse DNS lookup?

To reduce spam, many ISP mail server perform a reverse nslookup to validated the sender, nslookup - a DNS tool that Perform forward and reverse DNS queries for the current address to get the hostname of an IP address.

If your mail server IP address is 127.0.0.1 (an internal IP address) your mails are considered spam--will be rejected and becomes undeliverable in your mail server outbox--or, it may be accepted and deleted without being notified.

Therefore, the solution is to change the way your mail server computer identify itself to the remote mail server.

If you find that sending emails to AOL, Hotmail, Yahoo, and other similar Web-based email accounts does not work. Try changing the way your computer mail server identify itself to the remote mail server.

Most mail server program allows you to change "Server identity" for the HELO handshaking command.

For example, if your email address is me_@_myserver.com set the HELO handshaking command identification to mail.myserver.com or try it with just only: myserver.com
Notes: Use your own domain address and not the above examples.

Notes: Sending mails with the FROM: field email address that is different from the login IP address or not using an actual IP address may also result in having mails being rejected by the recipient mail server. If you are using a router, try using your router IP address.

AOL is known to check the sender email domain name, for example: from_@_mycompany.com against the HELO address during the handshaking identification.

Therefore, if you are using a hotmail or yahoo email address (at the FROM: field as sender address), AOL will reject the mail even though the FROM: field clearly identifies the sender.

AOL also does a reverse DNS lookup to ensure that the SMTP mail server and that is requesting to send a message actually exists as well as the email domain and IP's MX record and if there isn't one, mails are rejected or deleted as spam.

Every ISP have their own standards and ways to filter spam, therefore, by clearly identifying yourself at the FROM: field for most web-based email recipients like: Hotmail, Yahoo, etc., may not work with AOL or other ISPs or the other way round.

You may need to segregate your email address list, as well as to keep in mind that ISPs also limits accessibility to their mail server by time and quantity of mails. Therefore, you may need to experiment a bit by using a combination of different strategies for different popular web based email recipients.

Most of the time, it is usually due to your mail server identifying itself as an internal mail server IP address 127.0.0.1 which can be simply solved by using an actual exact IP address.

IP address is numeric numbers, for example: 151.196.75.10 and not mydomain.com See: Most common reason for undeliverable mails