In 2002 they said:
News Release
Symantec and Symbian Announce Partnership to Enhance Security Features for Symbian OS Smartphones
CUPERTINO, Calif. – July 30, 2002 – Symantec Corp., (Nasdaq: SYMC), the world leader in Internet security, and Symbian, the leading provider of operating systems for smartphones, today announced that they have signed an agreement that advances Symantec’s efforts to extend its range of award-winning Internet security solutions to Symbian OS smartphones.
Source
And now the company behind Norton Antivirus has a test program for Symantec Mobile Security.