QUASICONFORMAL EXTENSION OF MEROMORPHIC FUNCTIONS WITH NONZERO POLE

In this note, we consider meromorphic univalent functions f(z) in the unit disc with a simple pole at z = p is an element of (0, 1) which have a k-quasiconformal extension to the extended complex plane (C) over cap, where 0 <= k < 1. We denote the class of such functions by Sigma(k)(p). We first prove an area theorem for functions in this class. Next, we derive a sufficient condition for meromorphic functions in the unit disc with a simple pole at z = p is an element of(0, 1) to belong to the class Sigma(k)(p). Finally, we give a convolution property for functions in the class Sigma(k)(p).