When we add vendors in Banner Module it shows
"Error sending Mail to administrator"
"Error sending mail to vendors"
can anyone help please?

Have you configured the SMTP Server Settings on the Host Settings page? If you have, click the "Test" link there to see if your installation can actually send mail.

Thank you so much for your timely reply but again we are not sure about SMTP settings if we click test it shows

"There has been an error trying to send the test email. The error is:
The SMTP host was not specified."
Can you Help?

You need to fill in details of the SMTP server in that same section of the Host Settings page. If you are using a hosting service, you can ask them what should go there. If you are running your own mail system, somebody should tell you how to configure it.

Click the ? next to each item for quick help. The SMTP address is the most important. Fill in the IP address or the name of your SMTP server. This will be something like mail.mysite.com, smtp.mysite.com, etc. If you need to fill in a user name and password, do that and choose "basic" as the authentication type. These days, almost nobody uses anonymous authentication because it opens you up to outsiders using your site to send mail.

It may also be useful to check:How to set up email in DotNetNuke

Thank u