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Bull. Korean Math. Soc. 2020; 57(1): 133-138

Online first article December 17, 2019      Printed January 31, 2020

https://doi.org/10.4134/BKMS.b190126

Copyright © The Korean Mathematical Society.

Hyperbolically close to $Q_p^\#$-sequences

Rauno Aulaskari, Shamil Makhmutov, Jouni R\"atty\"a

University of Eastern Finland; Sultan Qaboos University; University of Eastern Finland

Abstract

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It is shown that each sequence lying sufficiently close in the hyperbolic sense to a $Q_p^\#$-sequence for a meromorphic function $f$ in the unit disc is also a $Q_p^\#$-sequence for~$f$.

Keywords: Normal function, $\N$-sequence, spherical derivative, $Q^\#_p$-class, $Q^\#_p$-sequence

MSC numbers: 30D45, 30D50

Supported by: This research was supported in part by Magnus Ehrnrooth Foundation, Ministerio de Econom´ıa y Competitivivad, Spain, projects MTM2014-52865-P and MTM2015-69323-REDT; La Junta de Andaluc´ıa, project FQM210; Academy of Finland project no. 268009.

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