There are four episodes in iCarly that feature mixed martial arts (MMA), and those episodes are iFight Shelby Marx (Carly fights Shelby in an CFC fight), iCook (Sam used an armbar on Ricky Flame), iPsycho (when Gibby was fighting Nora while deploying various fighting moves, such as takedowns and Judo throws) and iLook Alike (Jackson Colt is an MMA fighter). The writers of the show, in fact, did not use the incorrect term, "Ultimate Fighting," and did indeed call it, "mixed martial arts."
In iFight Shelby Marx, Carly and Shelby Marx (Victoria Justice) fight in a cage that is an octagon, which is a trademark of the Ultimate Fighting Championship (UFC). They fight in the CFC, which is actually the initials of a real MMA organization, the Cage Fighting Championship. Also, they do not use boxing gloves, but real MMA gloves.