Comptes Rendus
no. 21-22
Complex Analysis
An avoidance criterion for normal functions
Presented by: the Editorial Board
Yan Xu 1 ; Huiling Qiu 2
1 Institute of Mathematics, School of Mathematics, Nanjing Normal University, Nanjing 210046, PR China
2 Department of Applied Mathematics, Nanjing Audit University, Nanjing 210029, PR China
Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1159-1160

Let f be a meromorphic function in the unit disc Δ, φ1, φ2 and φ3 be three functions meromorphic in Δ and continuous on closure of Δ such that φi(z)≠φj(z) (1⩽i<j⩽3) on the unit circle |z|=1. If f(z)≠φi(z) (i=1,2,3) in Δ, then f is normal.

Soit f une fonction méromorphe dans le disque unité Δ, soient φ1, φ2 et φ3 trois fonctions méromorphes dans Δ et continues sur lʼadhérence de Δ et dont les restrictions au cercle unité sont deux à deux distinctes. Alors, si la fonction f est distincte des φi(z) (i=1,2,3), elle est normale.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2011.10.018

Yan Xu  1 ; Huiling Qiu  2

1 Institute of Mathematics, School of Mathematics, Nanjing Normal University, Nanjing 210046, PR China
2 Department of Applied Mathematics, Nanjing Audit University, Nanjing 210029, PR China 
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Yan Xu; Huiling Qiu. An avoidance criterion for normal functions. Comptes Rendus. Mathématique, Volume 349 (2011) no. 21-22, pp. 1159-1160. doi: 10.1016/j.crma.2011.10.018

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[2] O. Lehto; K.I. Virtanen Boundary behaviour and normal meromorphic functions, Acta Math., Volume 97 (1957), pp. 47-65

[3] A.J. Lohwater; Ch. Pommerenke On normal meromorphic functions, Ann. Acad. Sci. Fenn. Ser. A I Math., Volume 550 (1973) (12 pp)

[4] J. Schiff Normal Families, Springer-Verlag, New York/Berlin, 1993

[5] L. Yang Value Distribution Theory, Springer-Verlag & Science Press, Berlin, 1993

Cited by Sources:

☆ The first author is supported by NNSF of China (Grant Nos. 10871094; 11171045).

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