Transcendental entire functions of finite order sharing two sets of small functions with their shift differential operators

Year 2021, Volume: 50 Issue: 6, 1636 - 1651, 14.12.2021

Abhijit Banerjee , Arpıta Roy

https://doi.org/10.15672/hujms.785797

Abstract

Dealing with a question initiated by Liu [Meromorphic functions sharing a set with applications to difference equations, J. Math. Anal. Appl., 2009], we have investigated the situation when a finite order entire function and its shift differential operator share two sets of small functions. Our result has improved and extended the results of Chen-Chen [Entire functions sharing sets of small functions with their difference operators or shifts, Math. Slovaca, 2013] and Cui-Chen [The conjecture on unity of meromorphic functions concerning their differences, J. Difference Equ. Appl., 2016]. We have exhibited several examples relevant to the content of the paper.

Keywords

Entire functions, small function, uniqueness, reduced linear c-shift operator, finite order

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