The models listed above have a Liquid Crystal Display. By nature, LCD's are not susceptible to "burn in" technically but "image persistence." Leaving the screen on 24/7 is not considered proper operation and will void any warranty replacement terms. This is considered negligence in most cases. For your particular unit, reference the warranty terms at the end of the product's user guide.
Furthermore, a user may experience "dead pixels" which do not disappear, even after massaging the LCD.