JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (8): 78-85.doi: 10.6040/j.issn.1671-9352.0.2023.445

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Normal criterion concerning differential polynomials and omitted functions

YANG Qi, CHEN Pengbin, GONG Yihui   

  1. School of Mathematical Sciences, Xinjiang Normal University, Urumqi 830054, Xinjiang, China
  • Published:2025-07-25

Abstract: This paper studies the normal criterion of holomorphic functions involving exceptional functions and differential polynomials by using Pang-Zalcman lemma. A new normal criterion is obtained by extending the previous results through the method of proof by contradiction.

Key words: holomorphic functions, normal family, differential polynomials

CLC Number: 

  • O174.5
[1] LIU X J, YE Y S. A criterion of normality concerning holomorphic functions whose derivative omits a function[J]. Chinese Annals of Mathematics, 2011, 32(5):699-710.
[2] CHEN Q Y, LIU X J. A criterion of normality concerning holomorphic functions whose derivative omit a function II[J]. Chinese Annals of Mathematics, 2012, 33(6):815-822.
[3] 王雪,刘晓俊,陈巧玉. 涉及微分多项式及例外函数的正规定则[J]. 华东师范大学学报(自然科学版),2012,3:61-70. WANG Xue, LIU Xiaojun, CHEN Qiaoyu. Normal criterion concerning differential polynomials and omitted functions[J]. Journal of East China Normal University(Natural Science), 2012, 3:61-70.
[4] NIU P Y, XU Y. A normal criterion of families of holomorphic functions[J]. Analysis and Mathematical Physics, 2021, 11(3):1-10.
[5] XU Y. Normal families and fixed-points of meromorphic functions[J]. Monatshefte Für Mathematik, 2016, 179(3):471-485.
[6] 陈玮,王琼,袁文俊. 涉及Picard例外值的亚纯函数正规族[J]. 数学年刊A辑,2021,42(1):47-58. CHEN Wei, WANG Qiong, YUAN Wenjun. Normal families of meromorphic functions concerning Picard values and shared values[J]. Chinese Annals of Mathematics, Series A, 2021, 42(1):47-58.
[7] PANG X C, YANG D G, ZALCMAN L. Normal families of meromorphic functions whose derivatives omit a function[J]. Computational Methods and Function Theory, 2003, 2(1):257-265.
[8] FANG C Y, XU Y. Normal family of meromorphic functions concerning fixed-points[J]. Analysis and Mathematical Physics, 2019, 9(1):197-207.
[1] ZHANG Xiao-bin. Normality criteria of meromorphic functions for differential monomial sharing one value [J]. J4, 2013, 48(6): 29-33.
[2] QI Jian-ming1, DING Jie2, ZHU Tai-ying1. A note normal criterion about share values [J]. J4, 2011, 46(8): 63-67.
[3] LIU Shu-kuan. The normality criteria about f+a(z)(f ′)n [J]. J4, 2011, 46(1): 79-80.
[4] LI Xiao-lingsup> and HAN Qi . On a result of R.Bruck [J]. J4, 2007, 42(4): 84-90 .
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