UBI Research's president Lee Choong-hoon says that Apple is set to adopt OLEDs in its phones, and the company will release an iPhone with a curved OLED display in 2018. The curved iPhone will make up for 30% of total iPhone sales (about 100 million units) - but this will rise to 80% to 2020.
In fact, by 2021, Apple couple be the largest OLED customer - buying more OLEDs than Samsung Electronics. Samsung is currently using OLEDs in about 70% of its smartphones.
According to UBI, Samsung Display is the only company that can meet Apple's quality criteria for OLED displays - but Apple will want more suppliers and this will encourage LG and others to start producing OLEDs for Apple.
UBI says that Samsung's decision to supply OLEDs to Apple hints that Samsung does not see a way to increase smartphone sales - and if it cold sell more smartphones it would not supply to Apple.
This may be so, but it's also possible that Samsung is actually planning to introduce a foldable phone/tablet soon (the Galaxy X?), which may set the standard for a high-end mobile device. In that case Samsung will keep its premium display technology for itself - and supply older-gen curved (but not bendable) flexible OLED displays to its rivals (in fact it already started to do so).
