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A Class of Harmonic Meromorphic Functions of Complex Order

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Author(s): R. Ezhilarasi

Journal: Bonfring International Journal of Data Mining
ISSN 2250-107X

Volume: 02;
Issue: 02;
Start page: 22;
Date: 2012;
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Keywords: Harmonic Functions | Meromorphic Functions | Starlike Functions

ABSTRACT
The seminal work of Clunie and Sheil-Small [3] on harmonic mappings gave rise to studies on subclasses of complex-valued harmonic univalent functions. In this paper a class of harmonic meromorphic functions of the form f(z)=h(z)+g(z),|z| > 1 of complex order is introduced. It is shown that the functions in this class are sense preserving and univalent outside the unit disk. Sufficient coefficient 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.
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