According to the Korea Herald, Samsung Display has signed an agreement with Apple to supply flexible OLEDs for Apple's iPhone 9, due out in late 2018. The Korea Herald says that Apple will launch two iPhone 9 OLED models - with display sizes of 5.28" and 6.46". Of course the final display size is subject to change as the design of the iPhone 9 is not final yet.
SDC's total OLED shipments to Apple in 2018 will reach 180 million units, and Samsung will dedicate one of its upcoming flexible OLED fabs exclusively for Apple's displays.
Apple will start using OLED displays in its iPhone 8, due out in September 2017. Reports suggest that Samsung Display agreed to supply between 70 million to 100 million panels for the 2017 model.
According to some earlier reports, Apple was in talks with LG Display and also perhaps with BOE Display for future supply of OLED panels. If this latest Korea Herald claim is true, it means that Apple decided to rely solely on SDC for its 2018 OLED supply and may mean that LGD and BOE will not be ready in time with enough capacity (and maybe display quality) to support Apple.