A New Class of Univalent Harmonic Meromorphic Functions Defined by Multiplier Transformation

Abstract

The seminal work of Clunie and Sheil-Small [4] on harmonic mappings gave rise to studies on subclasses of complex valued harmonic univalent functions. In this paper we

introduced new family of analytical function functions of complex order in the open disk

f  z   h  z   g  z , which is harmonic meromorphic

U  z : z  1 defined by using modified Salagean

operator. It is shown that the functions in this class are sense preserving and univalent outside the unit disk. Sufficient conditions are obtained for functions in this class which are also shown to be

necessary when the co-analytic part

g  z has negative coefficients. We also obtain properties

such as distortion bounds, extreme points, convolution and convex combination for this class.