J. Korean Math. Soc. 2017; 54(1): 267-280
Online first article November 15, 2016 Printed January 1, 2017
https://doi.org/10.4134/JKMS.j150720
Copyright © The Korean Mathematical Society.
Ming Li and Toshiyuki Sugawa
Tohoku University, Tohoku University
In this paper, we study analytic and geometric properties of the solution $q(z)$ to the differential equation $q(z)+zq'(z)/q(z)=h(z)$ with the initial condition $q(0)=1$ for a given analytic function $h(z)$ on the unit disk $|z|<1$ in the complex plane with $h(0)=1.$ In particular, we investigate the possible largest constant $c>0$ such that the condition $|\Im[zf''(z)/f'(z)]| Keywords: open door lemma, subordination, convex function, strongly starlike function, dilogarithm function MSC numbers: 30C45, 30C80
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