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 ∈ (0, 1) which have a k-quasiconformal extension to the extended complex plane ℂ, where 0 ≤ k < 1. We denote the class of such functions by Σ_k(p). We first prove an area theorem for functions in this class. Next, we derive a sufficient condition for meromorphicT5 functions in the unit disc with a simple pole at z = p ∈ (0, 1) to belong to the class Σ_k(p). Finally, we give a convolution property for functions in the class Σ_k(p).