A geometric property for a class of meromorphic analytic functions
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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 , .
KeywordsAnalytic Function Geometric Property Unit Disk Meromorphic Function Conformal Mapping
Denote this class by .
2 Main result
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.
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