https:// or https://www. – SEO question

Hi all,

I have WordPress MU installed with multiple sites running on it. I have the domain mapping plugin installed so I can use https://www.mydomainnames.com. But when I goto these sites the www. then disappears. I have been posting on other sites and bookmarking sites with a bit of SEO in mind and have been using the www.

Anyone in a similar situation? Is it right for me to be using the www. as I have the domain mapping plugin? I want to do whatever is best SEO wise.

Thanks.