A user-defined function is owned by the user who created it; that user can execute it without privilege.
The owner of a user-defined function can grant privileges to other users with the GRANT EXECUTE command.
For example, the creator of the function fullname allows another_user to use fullname the function using:
GRANT EXECUTE ON fullname TO another_user
This statement revokes privilege to use the function:
REVOKE EXECUTE ON fullname FROM another_user
See Administration: User Management and Security > Security Management > Privileges > Object-Level Privileges > Grant and Revoke Object Level Privileges > Granting the EXECUTE Privilege on Functions and Procedures.