Taiwanese Journal of Mathematics

ON THE UNIQUENESS PROBLEMS OF ENTIRE FUNCTIONS AND THEIR DIFFERENCE OPERATORS

Huifang Liu and Zhiqiang Mao

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Abstract

In this paper, the uniqueness problems of entire functions and their difference operators are investigated. It is shown that if a finite order entire function $f$ shares $0,\alpha$ CM with its difference operator $\Delta_\eta f(z)=f(z+\eta)-f(z)$, then $\Delta_\eta f\equiv f$, where $\alpha$ is an entire function with order less than $f$. The research results also include a difference analogue of Brück conjecture, and extend some results in Chen-Yi Results Math., 63 (2013), 557-565).

Article information

Source
Taiwanese J. Math., Volume 19, Number 3 (2015), 907-917.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133668

Digital Object Identifier
doi:10.11650/tjm.19.2015.4674

Mathematical Reviews number (MathSciNet)
MR3353259

Zentralblatt MATH identifier
1357.30022

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory 39A10: Difference equations, additive

Keywords
entire function difference operator sharing value

Citation

Liu, Huifang; Mao, Zhiqiang. ON THE UNIQUENESS PROBLEMS OF ENTIRE FUNCTIONS AND THEIR DIFFERENCE OPERATORS. Taiwanese J. Math. 19 (2015), no. 3, 907--917. doi:10.11650/tjm.19.2015.4674. https://projecteuclid.org/euclid.twjm/1499133668


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