A Class of Harmonic Meromorphic Functions with Negative Coefficients

A class of complex-valued harmonic meromorphic functions of the form $f(z) = h(z)+\overline{g(z)}, |z| > 1,$ is introduced. It is shown that the functions in this class are orientation preserving and univalent outside the unit disk. Necessary and Sufficient coefficient conditions are obtained for functions in this class, which are also shown to be necessary when the co-analytic part g has negative coefficients. Distortion bounds, extreme points, convolution condition and convex combination are also obtained.