Quasiconformal extension of meromorphic functions with nonzero pole
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- by B. Bhowmik, G. Satpati and T. Sugawa
- Proc. Amer. Math. Soc. 144 (2016), 2593-2601
- DOI: https://doi.org/10.1090/proc/12933
- Published electronically: October 22, 2015
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Abstract:
In this note, we consider meromorphic univalent functions $f(z)$ in the unit disc with a simple pole at $z=p\in (0,1)$ which have a $k$-quasiconformal extension to the extended complex plane ${\widehat {\mathbb C}},$ where $0\leq k < 1$. We denote the class of such functions by $\Sigma _k(p)$. We first prove an area theorem for functions in this class. Next, we derive a sufficient condition for meromorphic functions in the unit disc with a simple pole at $z=p\in (0,1)$ to belong to the class $\Sigma _k(p)$. Finally, we give a convolution property for functions in the class $\Sigma _k(p)$.References
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Bibliographic Information
- B. Bhowmik
- Affiliation: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur - 721302, India
- MR Author ID: 828284
- ORCID: 0000-0001-9171-3548
- Email: bappaditya@maths.iitkgp.ernet.in
- G. Satpati
- Affiliation: Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur - 721302, India
- Email: g.satpati@iitkgp.ac.in
- T. Sugawa
- Affiliation: Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai 980-8579, Japan
- MR Author ID: 318760
- Email: sugawa@math.is.tohoku.ac.jp
- Received by editor(s): February 9, 2015
- Received by editor(s) in revised form: August 3, 2015
- Published electronically: October 22, 2015
- Additional Notes: The first author would like to thank NBHM, DAE, India (Ref.No.- 2/48(20)/2012/ NBHM(R.P.)/R&D II/14916) for its financial support
The third author would like to thank JSPS Grant-in-Aid for Scientific Research (B) 22340025 for its partial financial support - Communicated by: Jeremy Tyson
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2593-2601
- MSC (2010): Primary 30C62, 30C55
- DOI: https://doi.org/10.1090/proc/12933
- MathSciNet review: 3477076