Displaying 1161 – 1180 of 2730

Showing per page

On a subclass of α -uniform convex functions

Mugur Acu (2005)

Archivum Mathematicum

In this paper we define a subclass of α -uniform convex functions by using the S’al’agean differential operator and we obtain some properties of this class.

On a theorem of Haimo regarding concave mappings

Martin Chuaqui, Peter Duren, Brad Osgood (2011)

Annales UMCS, Mathematica

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.

On a theorem of Lindelöf

Vladimir Gutlyanskii, Olli Martio, Vladimir Ryazanov (2011)

Annales UMCS, Mathematica

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.

Currently displaying 1161 – 1180 of 2730