An avoidance criterion for normal functions

Yan Xu; Huiling Qiu

doi:10.1016/j.crma.2011.10.018

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.

Abstract
Résumé

Let f be a meromorphic function in the unit disc Δ, $φ_{1}$ , $φ_{2}$ and $φ_{3}$ be three functions meromorphic in Δ and continuous on closure of Δ such that $φ_{i} (z) \neq φ_{j} (z)$ ( $1 ⩽ i < j ⩽ 3$ ) on the unit circle $| z | = 1$ . If $f (z) \neq φ_{i} (z)$ ( $i = 1, 2, 3$ ) in Δ, then f is normal.

Soit f une fonction méromorphe dans le disque unité Δ, soient $φ_{1}$ , $φ_{2}$ et $φ_{3}$ 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 $φ_{i} (z)$ ( $i = 1, 2, 3$ ), elle est normale.

Received: 2011-07-28
Accepted: 2011-10-19
Published online: 2011-11-01

DOI: 10.1016/j.crma.2011.10.018

Author's affiliations:

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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     author = {Yan Xu and Huiling Qiu},
     title = {An avoidance criterion for normal functions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1159--1160},
     publisher = {Elsevier},
     volume = {349},
     number = {21-22},
     year = {2011},
     doi = {10.1016/j.crma.2011.10.018},
     language = {en},
}

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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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.10.018/

References
Cited by

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

[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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