What should I call someone addicted to mobile appliances?

Solution 1:

There's a CNN article about “smartphone zombies” that implies zombie is appropriate (perhaps in its sense “A person, usually undead, animated by unnatural forces ..., with no soul or will of his/her own”). The article also mentions Stephen King's novel, Cell:

... the protagonist, Clayton Riddell, doesn't turn into a zombie because he doesn't own a cell phone. The story is about an event called "The Pulse" that turns cell phone users into vicious, mindless beings.

Solution 2:

Apparently Nomophobia is the term commonly used for cell-phone addiction. It is an abbreviation of no mo-bile phone phobia

These are people who seldom switch off their cell-phones and start feeling stressed when forced to stay away from them.

It doesn't seem like there is any word for cell phone addiction. But this comes as close to it as possible.