Certain classes of the meromorphic harmonic functions with a pole at some fixed point of the unit disk

Abstract

The class S(H)(p), 0 <= p < 1, of complex valued, meromorphic harmonic univalent sense-preserving functions in the unit disk U\{p} is studied The functions belong to S(H)(p) have the expansion f(z) = a/z-p + Sigma(infinity)(n=0) c(n)z(n) + <(Sigma(infinity)(n=1) d(n)z(n))over bar> + A log vertical bar z - p vertical bar and (z -> p)limf(z) = infinity. Some coefficient estimates, distortion and area theorems are obtained. Sufficient coefficient conditions for a class of meromorphic harmonic univalent sense-preserving functions that are starlike and convex are given.