Open AccessEstimate for Schwarzian derivative of certain close-to-convex functions
Author(s) -
Zhenyong Hu,
Xiaoyuan Wang,
Jishan Fan
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2021626
Subject(s) - unit disk , schwarzian derivative , regular polygon , combinatorics , convex function , order (exchange) , mathematics , unit (ring theory) , physics , pure mathematics , geometry , finance , mathematics education , economics
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)\} > 0, $ $ \Re \{(1-z^{2})f'(z)\} > 0, $ $ \Re \{(1-z+z^{2})f'(z)\} > 0 $ and $ \Re \{(1-z)^{2}f'(z)\} > 0 $, we investigate the bounds for the first two consecutive derivatives of higher order Schwarzian derivatives of $ f(z) $.