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Monotonicity theorems for analytic functions centered at infinity


Author: Galatia Cleanthous
Journal: Proc. Amer. Math. Soc. 142 (2014), 3545-3551
MSC (2010): Primary 30C25, 30C35, 30C75
DOI: https://doi.org/10.1090/S0002-9939-2014-12084-3
Published electronically: June 23, 2014
MathSciNet review: 3238429
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Abstract: We consider the family of analytic functions centered at infinity with Laurent expansion $ f(z)=cz+c_{0}+\sum _{j=1}^{\infty }c_{j}z^{-j}.$ We prove some monotonicity theorems involving geometric quantities such as diameter, radius and length.


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Additional Information

Galatia Cleanthous
Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
Email: gkleanth@math.auth.gr

DOI: https://doi.org/10.1090/S0002-9939-2014-12084-3
Keywords: Meromorphic functions, conformal mapping, logarithmic capacity, monotonicity theorems, univalent functions, Schwarz Lemma.
Received by editor(s): October 19, 2012
Received by editor(s) in revised form: October 24, 2012, and October 29, 2012
Published electronically: June 23, 2014
Additional Notes: The author would like to thank D. Betsakos, her thesis advisor, for his help, and the Cyprus State Scholarship Foundation for its support.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2014 American Mathematical Society