The kind of specialized monitor used for cell phones with screens that wrap around the edges of the phone are flexible screens.
The flexible screens example is OLED screens. They are known to be made through the medium of organic materials that is said to often brings out light when electricity is said to be passed through it.
Note that the use of these screens do not need any form of backlights to function as they are produce to be thin enough to the give the place or point where they are said to be of flexible screens.
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