Uniqueness problems on difference operators of meromorphic functions

Chuangxin Chen^a, Ranran Zhang^b,*, Zhibo Huang^c, Shuangting Lan^d

ABSTRACT: In this paper, we study the shared-value problem of forward differences ∆c ƒ(z) and ∆_c ƒ(z) of a meromorphic function ƒ (z). For an entire function ƒ (z) with a Borel exceptional small function, we give the specific expression of ƒ(z) when ∆_c ƒ (z) and ∆_c ƒ (z) share a small function CM. For a meromorphic function ƒ (z) with a small deficient function, we obtain the relationship of ∆_c ƒ (z) and ∆_c ƒ(z) when they share a small function and ∞ CM.

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^a	College of Computational Sciences, Zhongkai University of Agriculture and Engineering, Guangzhou 510225 China
^b	Department of Mathematics, Guangdong University of Education, Guangzhou 510303 China
^c	School of Mathematical Sciences, South China Normal University, Guangzhou 510631 China
^d	School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665 China

* Corresponding author, E-mail: zhangranran@gdei.edu.cn

Received 19 Nov 2019, Accepted 9 Jun 2020

Uniqueness problems on difference operators of meromorphic functions

Chuangxin Chena, Ranran Zhangb,*, Zhibo Huangc, Shuangting Land

Chuangxin Chen^a, Ranran Zhang^b,*, Zhibo Huang^c, Shuangting Lan^d