A Subclass of Harmonic Univalent Functions with Varying Arguments Defined by Generalized Derivative Operator

where h and g are analytic in D. We call h the analytic part and g the coanalytic part of f . A necessary and sufficient condition for f to be locally univalent and sense preserving in D is that |h z | > |g z | for all z in D see 1 . Let H be the class of functions of the form 1.1 that are harmonic univalent and sense preserving in the unit disk U {z : |z| < 1} for which f 0 fz 0 − 1 0. Then for f h g ∈ H, we may express the analytic functions h and g as