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Let $f$ and $g$ be nonconstant meromorphic (entire, respectively) functions in the complex plane such that $f$ and $g$ are of finite order, let $a$ and $b$ be nonzero complex numbers and let $n$ be a positive integer satisfying $n\geq 21$ ($n\geq 12,$ respectively). We show that if the difference polynomials $f^n(z) + af(z+\eta)$ and $g^n(z) + ag(z+\eta)$ share $b$ CM, and if $f$ and $g$ share 0 and $\infty$ CM, where $\eta\neq 0$ is a complex number, then $f$ and $g$ are either equal or at least closely related. The results in this paper are difference analogues of the corresponding results from \cite{ref4}.
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참고문헌 (17)
참고문헌 신청
Z. X. Chen / 2014 / Complex Differences and Difference Equations / Science Press
Y.-M. Chiang / 2008 / On the Nevanlinna characteristic of f(z+${\eta}$ ) and difference equations in the complex plane / Ramanujan J. 16(1):105~129
W. Doeringer / 1982 / Exceptional values of differential polynomials / Pacific J. Math. 98(1):55~62
J. Grahl / 2011 / Differential polynomials and shared values / Ann. Acad. Sci. Fenn. Math. 36(1):47~70
R. G. Halburd / 2006 / Difference analogue of the lemma on the logarithmic derivative with applications to difference equations / J. Math. Anal. Appl. 314(2):477~487
Y.-M. Chiang / 2008 / On the Nevanlinna characteristic of f(z+
W. Doeringer / 1982 / Exceptional values of differential polynomials / Pacific J. Math. 98(1):55~62
J. Grahl / 2011 / Differential polynomials and shared values / Ann. Acad. Sci. Fenn. Math. 36(1):47~70
R. G. Halburd / 2006 / Difference analogue of the lemma on the logarithmic derivative with applications to difference equations / J. Math. Anal. Appl. 314(2):477~487
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