On angular derivatives of univalent functions

Univalent Functions with Univalent Derivatives. Ii

Univalent Functions Defined by Ruscheweyh Derivatives

We study some radii problems concerning the integral operator z F(z)y+l uY-I f(u) du zy o for certain classes, namely K and M (a), of univalent functions defined by Ruscheweyh n n derivatives. Infact, we obtain the converse of Ruscheweyh’s result and improve a result of Goel and Sohi for complex by a different technique. The results are sharp.

The norm of pre-Schwarzian derivatives on bi-univalent functions of order $alpha$

‎In the present investigation‎, ‎we give the best estimates for the norm of the pre-Schwarzian derivative $ T_{f}(z)=dfrac{f^{''}(z)}{f^{'}(z)} $ for bi-starlike functions and a new subclass of bi-univalent functions of order $ alpha $‎, ‎where‎ ‎$Vert T_{f} Vert= sup_{|z|

On Univalent Harmonic Functions

Two classes of univalent harmonic functions on unit disc satisfying the conditions ∑∞ n=2(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) and ∑∞ n=2 n(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) are given. That the ranges of the functions belonging to these two classes are starlike and convex, respectively. Sharp coefficient relations and distortion theorems are given for these functions. Furthermore results concerning th...

Boundary Angular Derivatives of Generalized Schur Functions

Characterization of generalized Schur functions in terms of their Taylor coefficients was established by M. G. Krein and H. Langer in [14]. We establich a boundary analog of this characterization.