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A note on the hyper-order of entire functions
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In the paper, we have two purposes. Firstly, we estimate the hyper-order of an entire function which shares two functions with it’s first derivative, and two examples are given to show the conclusion is sharp. Secondly, we generalize the Br¨uck conjecture with the idea of sharing functions.
Abstract
In the paper, we have two purposes. Firstly, we estimate the hyper-order of an entire function which shares two functions with it’s first derivative, and two examples are given to show the conclusion is sharp. Secondly, we generalize the Br¨uck conjecture with the idea of sharing functions.
참고문헌 (13)
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- A. Chen, "Value sharing of meromorphic functions and their derivatives", J. Math. Anal. Appl, 359(2), pp.696~703 (2009)
- Z. X. Chen, "Entire functions sharing fixed points with their higher order derivatives", Acta Math. Sinica, 50(6), pp.1213~1222 (2007)
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- X. M. Li, "Entire functions sharing one polynomial with their derivatives", Proc. Indian Acad. Sci. Math. Sci, 118(1), pp.13~26 (2008)
- X. J. Liu, "On the kth derivative of meromorphic functions with zeros of multiplicity at least k+1", J. Math. Anal. Appl, 348(1), pp.516~529 (2008)
- F. Lu, "Entire functions sharing polynomials with their first derivatives", Arch. Math, 92(6), pp.593~601 (2009)
- F. Lu, "On the uniqueness problems of meromorphic functions and their linear differential polynomials", J. Math. Anal. Appl, 362(2), pp.301~312 (2010)
- H. X. Yi, "Uniqueness Theory of Meromorphic Functions" (1995), Science Press
- J. Zhang, "On Bruck’s conjecture on entire functions sharing one value with their derivatives", Houston. J. Math, 36(2), pp.665~674 (2010)
관련 논문AI추천
On the entire function sharing one value cm with k-th derivatives손광호, Zong-Xuan Chen대한수학회 · 대한수학회지2005 · 제42권 제1호Meromorphic Functions Sharing a Nonzero Value with their DerivativesDa-Xiong Piao, Hong-Xun Yi, Rahman ullah, Xiao-Min Li경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제1호A note on the Bruck conjectureFeng Lu대한수학회 · 대한수학회보2011 · 제48권 제5호Meromorphic Functions Sharing a Small Function with their Differential PolynomialsJilong Zhang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제3호A Further Result Related to a Conjecture of R. BruckKai Liu, Lian-Zhong Yang, Nan Li경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제2호Uniqueness of Entire Functions that Share an Entire Function of Smaller Order with One of Their Linear Differential PolynomialsHong-Xun Yi, Xiao-Min Li경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제3호
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