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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].
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참고문헌 (17)
참고문헌 신청
A. Banerjee / 2007 / Uniqueness of meromorphic functions concerning differential monomials sharing the same value / Bull. Math. Soc. Sci 50:191~206
M. R. Chen / 2012 / Properties of difference polynomials of entire functions with finite order / Chinese Ann. Math. Ser. A 33:359~374
Y. M. Chiang / 2008 / On the Nevanlinna characteristic of f(z + η)and difference equations in the complex plane / Ramanujan J 16:105~129
R. G. Halburd / 2006 / Nevanlinna theory for the difference operator / Ann. Acad. Sci. Fenn. Math 31:463~478
R. G. Halburd / 2006 / Difference analogue of the lemma on the logarithmic derivative with application to difference equations / J. Math. Anal. Appl 314:477~487
M. R. Chen / 2012 / Properties of difference polynomials of entire functions with finite order / Chinese Ann. Math. Ser. A 33:359~374
Y. M. Chiang / 2008 / On the Nevanlinna characteristic of f(z + η)and difference equations in the complex plane / Ramanujan J 16:105~129
R. G. Halburd / 2006 / Nevanlinna theory for the difference operator / Ann. Acad. Sci. Fenn. Math 31:463~478
R. G. Halburd / 2006 / Difference analogue of the lemma on the logarithmic derivative with application to difference equations / J. Math. Anal. Appl 314:477~487
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