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Quasiconformal harmonic mappings and close-to-convex domains

Filomat ◽

10.2298/fil1001063k ◽

2010 ◽

Vol 24 (1) ◽

pp. 63-68 ◽

Cited By ~ 6

Author(s):

David Kalaj

Keyword(s):

Unit Disk ◽

Convex Domain ◽

Harmonic Mapping ◽

Harmonic Mappings ◽

Convex Domains ◽

Primary 30C55 ◽

Subject Classifications ◽

Mathematics Subject Classifications ◽

Secondary 31C05

Let f = h + ? be a univalent sense preserving harmonic mapping of the unit disk U onto a convex domain ?. It is proved that: for every a such that |a| < 1 (resp. |a| = 1) the mapping ?a = h + a? is an |a| quasiconformal (a univalent) close-to-convex harmonic mapping. This gives an answer to a question posed by Chuaqui and Hern?ndez (J. Math. Anal. Appl. (2007)). 2010 Mathematics Subject Classifications. Primary 30C55, Secondary 31C05. .

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RADIAL AND TANGENTIAL GROWTH OF CLOSE-TO-CONVEX FUNCTIONS

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091503000737 ◽

2005 ◽

Vol 48 (1) ◽

pp. 231-240 ◽

Cited By ~ 1

Author(s):

J. B. Twomey

Keyword(s):

Univalent Function ◽

Convex Functions ◽

Unit Disc ◽

Radial Growth ◽

Subject Classification ◽

Primary 30C55 ◽

Boundary Points

AbstractSome results are presented relating to questions raised in a recent paper by Anderson, Hayman and Pommerenke regarding the size of the set of boundary points of the unit disc at which a univalent function has a prescribed radial growth.AMS 2000 Mathematics subject classification: Primary 30C55