Korean J. Math.  Vol 28, No 4 (2020)  pp.889-906
DOI: https://doi.org/10.11568/kjm.2020.28.4.889

On the uniqueness of certain type of shift polynomials sharing a small function

Biswajit Saha

Abstract


In this article, we consider the uniqueness problem of the shift polynomials $f^{n}(z)(f^{m}(z)-1)\displaystyle\prod_{j=1}^{s} f(z+c_{j})^{\mu _{j}}$ and $f^{n}(z)(f(z)-1)^{m}\displaystyle\prod_{j=1}^{s} f(z+c_{j})^{\mu _{j}}$, where $f(z)$ is a transcendental entire function of finite order, $c_{j} (j=1, 2, ..., s)$ are distinct finite complex numbers and $n(\geq 1),$ $m(\geq 1),$ $s$ and $\mu _{j} (j=1, 2, ..., s)$ are integers. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo [Commun. Math. Stat. 3 (2015), 227-238]. 


Keywords


Uniqueness, Entire function, difference polynomial

Subject classification

30D35, 39A10

Sponsor(s)



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References


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