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Uniqueness of Entire Functions that Share an Entire Function of Smaller Order with One of Their Linear Differential Polynomials

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We prove a uniqueness theorem of entirefunctions sharing an entire function of smaller order with their linear differential polynomials. The results in this paper improve the corresponding results given by Gundersen-Yang[4], Chang-Zhu[3], and others. Some examples are provided to show that the results inthis paper are best possible.

Abstract

We prove a uniqueness theorem of entirefunctions sharing an entire function of smaller order with their linear differential polynomials. The results in this paper improve the corresponding results given by Gundersen-Yang[4], Chang-Zhu[3], and others. Some examples are provided to show that the results inthis paper are best possible.

참고문헌 (13)

  1. A. Al-Khaladi, "On meromorphic functions that share one value with their derivative", Analysis, 25, pp.131~140 (2005)
  2. R. Bruck, "On entire functions which share one value CM with their first derivative", Results in Math., 30, pp.21~24 (1996)
  3. J. M. Chang, "Entire functions that share a small function with their derivatives", J. Math. Anal. Appl., 351, pp.491~496 (2009)
  4. G. G. Gundersen, "Entire functions that share one value with one or two of their derivatives", J. Math. Anal. Appl., 223, pp.88~95 (1998)
  5. W. K. Hayman, "Meromorphic Functions" (1964), The Clarendon Press
  6. G. Jank, "Einfuhrung in die Theorie der ganzen und meromorphen Funktionen mit Anwendungen auf Differentialgleichungen" (1985), Birkhauser
  7. I. Laine, "Nevanlinna Theory and Complex Differential Equations" (1993), Walter de Gruyter
  8. L. Rubel, "Values shared by an entire function and its derivative", (Proc.Conf.), Lecture Notes in Mathematics, 599, pp.101~103 (1977), Springer-Verlag
  9. G. Valiron, "Lectures on the General Theory of Integral Functions" (1923), Edouarard Privat
  10. J. Wang, "Uniqueness of entire functions and their derivatives", Computational Methods and Function Theory, 8, pp.327~338 (2008)
  11. L. Yang, "Value Distribution Theory" (1993), Science Press
  12. C. C. Yang, "Uniqueness Theory of Meromorphic Functions" (2003), Kluwer Academic Publishers
  13. J. H. Zheng, "Value Distibution of Meromorphic Funtions" (2011), Springer-Verlag

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