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

Previous Articles     Next Articles

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

PDF (PC)

55

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 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd