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Article


Title

Normal families and shared functions

Authors

Year of publication

2018

Published in

Fasciculi Mathematici

Journal year: 2018 | Journal number: nr 60

Article type

scientific article

Publication language

english

Keywords
EN
  • meromorphic function
  • normal criterion
  • Shared function
Abstract

EN Let k ϵ N, m ϵ N ∪ {0}, and let a(z)( ≢ 0) be a holomorphic function, all zeros of a(z) have multiplicities at most m. Let F be a family of meromorphic functions in D. If for each f ϵ F, the zeros of f have multiplicities at least k + m + 1 and all poles of f are of multiplicity at least m +1, and for f, g ϵ F, ff(k) - a(z) and gg(k) - a(z) share 0, then F is normal in D. Some examples are given to show that the conditions are best, and the result removes the condition “m is an even integer” in the result due to Sun [Kragujevac Journal of Math 38(2), 173-282, 2014].

Pages (from - to)

173 - 180

DOI

10.1515/fascmath-2018-0011

License type

CC BY-NC-ND (attribution - noncommercial - no derivatives)

Full text of article

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Access level to full text

public

Points of MNiSW / journal

10.0

Points of MNiSW / journal in years 2017-2021

10.0

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