A criterion for bounded functions
Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 215-225
Printed January 31, 2016
Mamoru Nunokawa, Shigeyoshi Owa, and Janusz Sok\'{o}\l
University of Gunma, Kinki University, Rzesz\'{o}w University of Technology
Abstract : We consider a sufficient condition for $w(z)$, analytic in $|z|<1$, to be bounded in $|z|<1$, where $w(0)=w'(0)=0$. We apply it to the meromorphic starlike functions. Also, a certain Briot-Bouquet differential subordination is considered. Moreover, we prove that if $p(z)+zp'(z)\phi(p(z))\prec h(z)$, then $p(z)\prec h(z)$, where $h(z)=[(1+z)(1-z)]^{\alpha}$, under some additional assumptions on $\phi(z)$.
Keywords : analytic, meromorphic, convex, starlike, univalent, Nunokawa's lemma, Briot-Bouquet, differential subordination
MSC numbers : Primary 30C45; Secondary 30C80
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd