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Let $f$ be a nonconstant meromorphic function of hyper order strictly less than $1$, and let $c$ be a nonzero finite complex number such that $f(z+c)\not\equiv f(z)$. We prove that if $\Delta_{c} f=f(z+c)-f(z)$ and $f$ share $0,\infty$ CM and $1$ IM, then $\Delta_{c} f= f$. Our result generalizes and greatly improves the related results.
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참고문헌 (13)
참고문헌 신청
Shengjiang Chen / 2018 / On Uniqueness of Meromorphic Functions and Their Difference Operators with Partially Shared Values / Computational Methods and Function Theory 18(3):529~536
Zong-Xuan Chen / 2013 / On Sharing Values of Meromorphic Functions and Their Differences / Results in Mathematics 63(1-2):557~565
Yik-Man Chiang / 2008 / On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane / The Ramanujan Journal 16(1):105~129
F. Gross / 1976 / Complex analysis / Springer :51~67
R.G. Halburd / 2006 / Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations / Journal of Mathematical Analysis and Applications 314(2):477~487
Zong-Xuan Chen / 2013 / On Sharing Values of Meromorphic Functions and Their Differences / Results in Mathematics 63(1-2):557~565
Yik-Man Chiang / 2008 / On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane / The Ramanujan Journal 16(1):105~129
F. Gross / 1976 / Complex analysis / Springer :51~67
R.G. Halburd / 2006 / Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations / Journal of Mathematical Analysis and Applications 314(2):477~487
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