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On a radius problem concerning a class of close-to-convex functions

Richard Fournier (1995)

Banach Center Publications

The problem of estimating the radius of starlikeness of various classes of close-to-convex functions has attracted a certain number of mathematicians involved in geometric function theory ([7], volume 2, chapter 13). Lewandowski [11] has shown that normalized close-to-convex functions are starlike in the disc | z | < 4 √ 2 - 5 . Krzyż [10] gave an example of a function f ( z ) = z + ∑ n = 2 ∞ a n z n , non-starlike in the unit disc , and belonging to the class H = f | f’() lies in the right half-plane. More generally let H* = f | f’() lies in...

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.

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