Normality and attracting fixed points | Zendy

Chang Jianming | Zendy; Fang Mingliang | Zendy; Zalcman Lawrence | Zendy

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Normality and attracting fixed points

Author(s) -

Chang Jianming,

Fang Mingliang,

Zalcman Lawrence

Publication year - 2008

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/blms/bdn056

Subject(s) - meromorphic function , iterated function , mathematics , fixed point , normality , domain (mathematical analysis) , integer (computer science) , unit (ring theory) , complex plane , plane (geometry) , construct (python library) , unit circle , pure mathematics , combinatorics , discrete mathematics , mathematical analysis , geometry , computer science , statistics , mathematics education , programming language

Let k ⩾ 2 be a fixed integer. We construct a non‐normal family of meromorphic functions in the unit disc with k th iterates that have no non‐attracting fixed points in the unit disc. We also prove that a family of meromorphic functions in a plane domain is normal if all fixed points in the domain of the k ‐iterates of all functions in the family are uniformly attracting.

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