On the analytic part of harmonic univalent functions
Bull. Korean Math. Soc. 2005 Vol. 42, No. 3, 563-569
Printed September 1, 2005
Basem Aref Frasin
Al al-Bayt University
Abstract : In [2], Jahangiri studied the harmonic starlike functions of order $\alpha ,$ and he defined the class $\mathcal{T}_{\mathcal{H}% }(\alpha )$ consisting of functions $f=h+\bar{g}$ where $h$ and $g$ are the analytic and the co-analytic part of the function $f,$ respectively. In this paper, we introduce the class $\mathcal{T}_{\mathcal{H}}(\alpha ,\beta )$ of analytic functions and prove various coefficient inequalities, growth and distortion theorems, radius of convexity for the function $h,$ if the function $f$ belongs to the classes $\mathcal{T}_{\mathcal{H}}(\alpha )$ and $\mathcal{T}_{\mathcal{H}}(\alpha ,\beta ).
Keywords : harmonic, analytic and univalent functions
MSC numbers : 30C45
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