scholarly journals HARMONIC MAPPINGS RELATED TO FUNCTIONS WITH BOUNDED BOUNDARY ROTATION AND NORM OF THE PRE-SCHWARZIAN DERIVATIVE

2014 ◽  
Vol 51 (3) ◽  
pp. 803-812 ◽  
Author(s):  
Stanis lawa Kanas ◽  
Dominika Klimek-Smet
Keyword(s):  
Schwarzian Derivative ◽  
Harmonic Mappings ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

On the class of harmonic mappings which is related to the class of bounded boundary rotation

2015 ◽  
Vol 267 ◽  
pp. 790-794
Author(s):  
Yaşar Polatog̃lu ◽  
Melike Aydog̃an ◽  
Yasemin Kahramaner
Keyword(s):  
Harmonic Mappings ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

scholarly journals Harmonic mappings of bounded boundary rotation

2017 ◽  
Vol 146 (3) ◽  
pp. 1113-1121 ◽  
Author(s):  
D. Bshouty ◽  
A. Lyzzaik ◽  
F. M. Sakar
Keyword(s):  
Harmonic Mappings ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

Harmonic mappings related to the bounded boundary rotation

2014 ◽  
Vol 8 ◽  
pp. 2837-2843
Author(s):  
Asena Cetinkaya ◽  
Yasemin Kahramaner ◽  
Yasar Polatoglu
Keyword(s):  
Harmonic Mappings ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

The Schwarzian derivative for harmonic mappings

2003 ◽  
Vol 91 (1) ◽  
pp. 329-351 ◽  
Author(s):  
Martin Chuaqui ◽  
Peter Duren ◽  
Brad Osgood
Keyword(s):  
Schwarzian Derivative ◽  
Harmonic Mappings

Multivalent and Meromorphic Functions of Bounded Boundary Rotation

1975 ◽  
Vol 27 (1) ◽  
pp. 186-199 ◽  
Author(s):  
Ronald J. Leach
Keyword(s):  
Critical Points ◽  
Analytic Functions ◽  
Unit Disc ◽  
Meromorphic Functions ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation

The classVk(p). We generalize the class Vk of analytic functions of bounded boundary rotation [8] by allowing critical points in the unit disc U.Definition. Let f(z) = aqzq + . . . (q 1) be analytic in U. Then f(z) belongs to the class Vk(p) if for r sufficiently close to 1,andWe note that (1.1) implies that / has precisely p — 1 critical points in U.

Coefficients of Symmetric Functions of Bounded Boundary Rotation

1974 ◽  
Vol 26 (6) ◽  
pp. 1351-1355 ◽  
Author(s):  
Ronald J. Leach
Keyword(s):  
Unit Disc ◽  
Symmetric Functions ◽  
The Family ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Image Position

Let denote the family of all functions of the formthat are analytic in the unit disc U, f′(z) ≠ 0 in U and f maps U onto a domain of boundary rotation at most . Recently Brannan, Clunie and Kirwan [2] and Aharonov and Friedland [1] have solved the problem of estimating |amp+1| for all , provided m = 1.

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