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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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  4. A. Chen, "Value sharing of meromorphic functions and their derivatives", J. Math. Anal. Appl, 359(2), pp.696~703 (2009)
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  7. I. Laine, "Nevanlinna Theory and Complex Differential Equations, In de Gruyter Studies in Mathematics, 15" (1993), Walter de Gruyter & Co.
  8. X. M. Li, "Entire functions sharing one polynomial with their derivatives", Proc. Indian Acad. Sci. Math. Sci, 118(1), pp.13~26 (2008)
  9. 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)
  10. F. Lu, "Entire functions sharing polynomials with their first derivatives", Arch. Math, 92(6), pp.593~601 (2009)
  11. F. Lu, "On the uniqueness problems of meromorphic functions and their linear differential polynomials", J. Math. Anal. Appl, 362(2), pp.301~312 (2010)
  12. H. X. Yi, "Uniqueness Theory of Meromorphic Functions" (1995), Science Press
  13. J. Zhang, "On Bruck’s conjecture on entire functions sharing one value with their derivatives", Houston. J. Math, 36(2), pp.665~674 (2010)

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