Supporting one-handed interaction on touch screen devices is a challenge. Two of the biggest design challenges for touch screen devices are single-handed operation and haptic response. The Human-Computer Interaction Lab at the University of Maryland is researching the one-handed challenge.
“We are developing interfaces to support one-handed use of small devices. Most cell phones already support one-handed use, but most lack touch screens and thus interaction is limited to keypad-mapped menus and directional navigation. Personal Digital Assistants (PDAs) on the other hand, do have touch sensitive displays, but are poor at supporting one-handed use for two main reasons. The first is that software interfaces for PDAs typically feature input targets that are too small for finger tip actuation, thus requiring a stylus, and two hands to use. The second reason is that the entire screen is valid for user input, which typically exceeds the extent of the thumb when held in one hand.”
Link: Interfaces Supporting One-Handed Use of Small Devices (cs.umd.edu)