Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2020; 57(5): 1307-1317

Online first article July 31, 2020      Printed September 30, 2020

https://doi.org/10.4134/BKMS.b190998

Copyright © The Korean Mathematical Society.

Uniqueness theorem for a meromorphic function and its exact difference

Shengjiang Chen, Aizhu Xu

Ningde Normal University; Ningde Normal University

Abstract

Let $f$ be a nonconstant meromorphic function of hyper order strictly less than $1$, and let $c$ be a nonzero finite complex number such that $f(z+c)\not\equiv f(z)$. We prove that if $\Delta_{c} f=f(z+c)-f(z)$ and $f$ share $0,\infty$ CM and $1$ IM, then $\Delta_{c} f= f$. Our result generalizes and greatly improves the related results.

Keywords: Meromorphic, exact difference, uniqueness, shared values

MSC numbers: Primary 30D35, 39A10

Supported by: This work was supported by the NNSF of China (No. 11801291), the Natural Science Foundation of Fujian (No. 2018J01424), the Training Program of Outstanding Youth Research Talents in Fujian (2018) and the project of Ningde Normal University (2019T01)