Taiwan's Digitimes reports that local equipment suppliers are seeing increased orders from Samsung and LG for components used in smartphones with flexible displays. These orders are "mostly" for Samsung's Galaxy Round and LG's G Flex (which hints that perhaps there are new phones with flexible displays on the way).
The Taiwanese suppliers say that most phone vendors are focusing on low-priced units, but Samsung is actually looking to further its presence in the high-end market. This contrasts with a previous report from Korea that claims that Samsung is focusing on lower-end mobile phones that use LCD displays.
We do know that both LG and Samsung expect flexible OLEDs to grab 40% of the mobile phone display market by 2018 - that's only 4 years from now. The 40% estimate actually comes from DisplaySearch.