Bulletin of the
Korean Mathematical Society
BKMS

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

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Bull. Korean Math. Soc. 2023; 60(2): 461-473

Online first article March 21, 2023      Printed March 31, 2023

https://doi.org/10.4134/BKMS.b220190

Copyright © The Korean Mathematical Society.

Uniqueness results on meromorphic functions and their difference operators sharing targets with weight

Thu Thuy Hoang, Hong Nhat Nguyen, Duc Thoan Pham

55 Giai Phong str., Hai Ba Trung; 207 Giai Phong str., Hai Ba Trung; 55 Giai Phong str., Hai Ba Trung

Abstract

Let $f$ be a nonconstant meromorphic function of hyper-order strictly less than 1, and let $c\in\mathbb C\setminus\{0\}$ such that $f(z + c) \not\equiv f(z)$. We prove that if $f$ and its exact difference $\Delta_cf(z) = f(z + c) - f(z)$ share partially $0, \infty$ CM and share 1 IM, then $\Delta_cf = f$, where all 1-points with multiplicities more than 2 do not need to be counted. Some similar uniqueness results for such meromorphic functions partially sharing targets with weight and their shifts are also given. Our results generalize and improve the recent important results.

Keywords: Meromorphic functions, sharing targets with weight, uniqueness theorems

MSC numbers: Primary 32A22, 32H30; Secondary 30D35

Supported by: The authors wish to express their thanks to the reviewer for his/her valuable suggestions and comments which help us improve the paper. This research is funded by Hanoi University of Civil Engineering (HUCE) under grant number 16-2022/KHXD-T\Dbar.