Some results on complex differential-difference analogue of Bruck conjecture
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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 $f(z+\eta)-f(z)\not\equiv 0$.
Abstract
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 $f(z+\eta)-f(z)\not\equiv 0$.
참고문헌 (16)
- W. Bergweiler, "Zeros of difference of meromorphic functions", Math. Proc. Cambridge Philos. Soc, 142(1), pp.133~147 (2007)
- R. Br¨uck, "On entire functions which share one value CM with their first derivative", Results Math, 30(1-2), pp.21~24 (1996)
- Z. X. Chen, "On the difference counterpart of Br¨uck’s conjecture", Acta. Math. Sci. Ser. B Engl. Ed, 34(3), pp.653~659 (2014)
- Z. X. Chen, "On sharing values of meromorphic functions and their differences", Results Math, 63(1-2), pp.557~565 (2013)
- Y. M. Chiang, "On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane", Ramanujan J, 16(1), pp.105~129 (2008)
- G. Gundersen, "Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates", J. London Math. Soc, 37(1), pp.88~104 (1988)
- G. Gundersen, "Entire functions that share one value with one or two of their derivatives", J. Math. Anal. Appl, 223(1), pp.88~95 (1998)
- W. K. Hayman, "Slowly growing integral and subharmonic functions", Comment. Math. Helv, 34, pp.75~84 (1960)
- W. K. Hayman, "Meromorphic Function" (1964), Clarendon Press
- J. Heittokangas, "Value sharing results for shifts of meromorphic functions, and sufficient conditions for perodicity", J. Math. Anal. Appl, 355(1), pp.352~363 (2009)
- I. Laine, "Nevanlinna Theory and Complex Differential Equations" (1993), W. de Gruyter
- S. Li, "Entire functions sharing one or two finite values CM with their shifts or difference operator", Arch. Math, 97(5), pp.475~483 (2011)
- S. Li, "Erratum to : A note on Br¨uck’s Conjecture", Arch. Math, 99(3), pp.255~259 (2012)
- X. M. Li, "Entire functions sharing an entire function of smaller order with their difference operator", Acta. Math. Sin. (Engl. Ser.), 30(3), pp.481~498 (2014)
- Kai Liu, "Some results related to complex differential-difference equations of certain types", 대한수학회보, 51(5), pp.1453~1467 (2014), 대한수학회
- C. C. Yang, "Uniqueness Theory of Meromorphic Functions" (2003), Kluwer Academic