Open AccessThe zeros of f^{n}f^(k)-a and normal families of meromorphic functions
Author(s) -
sun xiong
Publication year - 2020
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.51.2020.3041
Subject(s) - meromorphic function , mathematics , multiplicity (mathematics) , normality , combinatorics , function (biology) , normal family , constant (computer programming) , discrete mathematics , pure mathematics , mathematical analysis , statistics , computer science , evolutionary biology , biology , programming language
In this paper, we first prove that if f be a non-constant meromorphic function, all of whose zeros have multiplicity at least $k$, then f^{n}f^{(k)}-a has at least m+1 distinct zeros, where $k(\geq2),m(\geq1),n(\geq m+1)$ are three integers, and $a\in \mathbb{C}\cup\setminus\{0\}$.Also, in relation to this result, a normality criteria is given, which extends the related result.