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In this paper, we utilize the Nevanlinna theory and uniqueness theory of meromorphic function to investigate the differential-diff\-erence analogue of Br\"{u}ck conjecture. In other words, we consider \linebreak $\Delta_{\eta}f(z)=f(z+\eta)-f(z)$ and $f'(z)$ share one value or one small function, and then obtain the precise expression of transcendental entire function $f(z)$ under certain conditions, where $\eta\in \mathbb{C}\setminus \{0\}$ is a constant such that $f(z+\eta)-f(z)\not\equiv 0$.
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참고문헌 (16)
참고문헌 신청
C. C. Yang / 2003 / Uniqueness Theory of Meromorphic Functions / Kluwer Academic
G. Gundersen / 1988 / Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates / J. London Math. Soc 37 (1) : 88 ~ 104
G. Gundersen / 1998 / Entire functions that share one value with one or two of their derivatives / J. Math. Anal. Appl 223 (1) : 88 ~ 95
I. Laine / 1993 / Nevanlinna Theory and Complex Differential Equations / W. de Gruyter
J. Heittokangas / 2009 / Value sharing results for shifts of meromorphic functions, and sufficient conditions for perodicity / J. Math. Anal. Appl 355 (1) : 352 ~ 363
G. Gundersen / 1988 / Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates / J. London Math. Soc 37 (1) : 88 ~ 104
G. Gundersen / 1998 / Entire functions that share one value with one or two of their derivatives / J. Math. Anal. Appl 223 (1) : 88 ~ 95
I. Laine / 1993 / Nevanlinna Theory and Complex Differential Equations / W. de Gruyter
J. Heittokangas / 2009 / Value sharing results for shifts of meromorphic functions, and sufficient conditions for perodicity / J. Math. Anal. Appl 355 (1) : 352 ~ 363
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