- Open Access
A geometric property for a class of meromorphic analytic functions
© Ibrahim and Sokó¿; licensee Springer. 2014
- Received: 22 February 2014
- Accepted: 13 March 2014
- Published: 26 March 2014
In this paper, we investigate a geometric property of a class of meromorphic functions. This property implies concavity. A sufficient condition, for a function in this class, is considered utilizing Jack’s lemma. We show that, for a meromorphic function , the sufficient condition for concavity is , .
- Analytic Function
- Geometric Property
- Unit Disk
- Meromorphic Function
- Conformal Mapping
Denote this class by .
We have the following result.
then f is concave in .
This contradicts the assumption (2.1). Therefore, in U and (2.2) means that f is concave. □
This work is supported by University of Malaya High Impact Research Grant no vote UM.C/625/HIR/MOHE/SC/13/2 from Ministry of Higher Education Malaysia. The authors also would like to thank the referees for giving useful suggestions for improving the work.
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.