On a subclass of analytic functions defined by Ruscheweyh derivative and generalized Sălăgean operator.
In this paper we define a subclass of -uniform convex functions by using the S’al’agean differential operator and we obtain some properties of this class.
In this paper we discuss some subordination results for a subclass of functions analytic in the unit disk U
A relatively simple proof is given for Haimo's theorem that a meromorphic function with suitably controlled Schwarzian derivative is a concave mapping. More easily verified conditions are found to imply Haimo's criterion, which is now shown to be sharp. It is proved that Haimo's functions map the unit disk onto the outside of an asymptotically conformal Jordan curve, thus ruling out the presence of corners.
We give a quasiconformal version of the proof for the classical Lindelöf theorem: Let f map the unit disk D conformally onto the inner domain of a Jordan curve C. Then C is smooth if and only if arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.