Bull. Korean Math. Soc. 2020; 57(5): 1259-1267
Online first article March 3, 2020 Printed September 30, 2020
https://doi.org/10.4134/BKMS.b190934
Copyright © The Korean Mathematical Society.
Kai Liu, Yuming Wei, Peiyong Yu
Nanchang University; Nanchang University; Nanchang University
On the periodicity of transcendental entire functions, Yang's Conjecture is proposed in \cite{lilvyang, wanghu}. In the paper, we mainly consider and obtain partial results on a general version of Yang's Conjecture, namely, if $f(z)^{n}f^{(k)}(z)$ is a periodic function, then $f(z)$ is also a periodic function. We also prove that if $f(z)^{n}+f^{(k)}(z)$ is a periodic function with additional assumptions, then $f(z)$ is also a periodic function, where $n,k$ are positive integers.
Keywords: Entire functions, periodicity, differential-difference equations
MSC numbers: Primary 30D35, 39A05
Supported by: This work was partially supported by the NSFC (No.11661052), the outstanding youth scientist foundation plan of Jiangxi (No. 20171BCB23003)
2020; 57(4): 1033-1048
2019; 56(1): 45-56
2018; 55(2): 469-478
2014; 51(5): 1453-1467
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd