Complex Analysis
An avoidance criterion for normal functions
[Un critère dʼévitement pour des familles normales]
Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1159-1160.

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.

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) (1i<j3) on the unit circle |z|=1. If f(z)φi(z) (i=1,2,3) in Δ, then f is normal.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.10.018
Xu, Yan 1 ; Qiu, Huiling 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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Xu, Yan; Qiu, Huiling. An avoidance criterion for normal functions. Comptes Rendus. Mathématique, Tome 349 (2011) no. 21-22, pp. 1159-1160. doi : 10.1016/j.crma.2011.10.018. http://www.numdam.org/articles/10.1016/j.crma.2011.10.018/

[1] Lappan, P. Avoidance criteria for normal families and normal functions, Berlin, 2001, World Sci. Publ., River Edge, NJ (2003), pp. 221-228

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

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

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

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

Cité par Sources :

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