Hohlov Effects for Pre-Schwarzian Derivatives of Functions in the Gakhov Class

2019 ◽  
Vol 40 (9) ◽  
pp. 1324-1329
Author(s):  
A. V. Kazantsev
2011 ◽  
Vol 36 ◽  
pp. 449-460 ◽  
Author(s):  
Martin Chuaqui ◽  
Peter Duren ◽  
Brad Osgood

2010 ◽  
Vol 5 (3) ◽  
pp. 659-670 ◽  
Author(s):  
Seong-A Kim ◽  
Toshiyuki Sugawa

2013 ◽  
Vol 25 (1) ◽  
pp. 64-91 ◽  
Author(s):  
Rodrigo Hernández ◽  
María J. Martín

2006 ◽  
Vol 49 (1) ◽  
pp. 131-143 ◽  
Author(s):  
Yong Chan Kim ◽  
Toshiyuki Sugawa

AbstractA sharp norm estimate will be given to the pre-Schwarzian derivatives of close-to-convex functions of specified type. In order to show the sharpness, we introduce a kind of maximal operator which may be of independent interest. We also discuss a relation between the subclasses of close-to-convex functions and the Hardy spaces.


2021 ◽  
Vol 6 (10) ◽  
pp. 10778-10788
Author(s):  
Zhenyong Hu ◽  
◽  
Xiaoyuan Wang ◽  
Jinhua Fan ◽  

<abstract><p>Let $ f(z) $ be analytic in the unit disk with $ f(0) = f'(0)-1 = 0 $. For the following close-to-convex subclasses: $ \Re \{(1-z)f'(z)\} &gt; 0, $ $ \Re \{(1-z^{2})f'(z)\} &gt; 0, $ $ \Re \{(1-z+z^{2})f'(z)\} &gt; 0 $ and $ \Re \{(1-z)^{2}f'(z)\} &gt; 0 $, we investigate the bounds for the first two consecutive derivatives of higher order Schwarzian derivatives of $ f(z) $.</p></abstract>


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