A Class of Complex-valued Harmonic Functions Defined by Dziok-Srivastava Operator

Ramasamy Chandrashekar; Gangadharan Murugusundaramoorthy; See Keong Lee; Kumbakonam Govindarajan Subramanian

Authors

Ramasamy Chandrashekar
Gangadharan Murugusundaramoorthy
See Keong Lee
Kumbakonam Govindarajan Subramanian

Keywords:

Harmonic functions, Hypergeometric functions, Dziok-Srivastava operator, extreme points, integral operator

Abstract

The Dziok-Srivastava [6] operator introduced in the study of analytic functions and associated with generalized hypergeometric functions has been extended to harmonic mappings [2, 12]. Using this operator we introduce a subclass of the class $gif.latex?\mathcal{H}$ of complex-valued harmonic univalent functions $gif.latex?f&space;=&space;h&space;+&space;\bar{g}$ where $gif.latex?h$ is the analytic part and $gif.latex?g$ is the co-analytic part of $gif.latex?f$ in $gif.latex?|z|$ ^< $gif.latex?1$ . Coefficient bounds, extreme points, inclusion results and closure under an integral operator for this class are obtained.

A Class of Complex-valued Harmonic Functions Defined by Dziok-Srivastava Operator

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