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Value sharing results of a meromorphic function f(z) and f(qz)

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In this paper, we investigate sharing value problems related to a meromorphic function f(z) and f(qz), where q is a non-zero constant. It is shown, for instance, that if f(z) is zero-order and shares two valves CM and one value IM with f(qz), then f(z)=f(qz).

Abstract

In this paper, we investigate sharing value problems related to a meromorphic function f(z) and f(qz), where q is a non-zero constant. It is shown, for instance, that if f(z) is zero-order and shares two valves CM and one value IM with f(qz), then f(z)=f(qz).

참고문헌 (11)

  1. D. C. Barnett, "Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations", Proc. Roy. Soc. Edinburgh Sect. A, 137(3), pp.457~474 (2007)
  2. A. A. Goldberg, "Value Distribution of Meromorphic Functions", Transl. Math. Monogr, 236 (2008), American Mathematical Society, Providence, RI
  3. G. G. Gundersen, "Meromorphic functions that share three or four values", J. London Math. Soc. (2), 20(3), pp.457~466 (1979)
  4. G. G. Gundersen, "Meromorphic functions that share four values", Trans. Amer. Math. Soc, 277(2), pp.545~567 (1983)
  5. W. Hayman, "Meromorphic Functions" (1964), Clarendon Press
  6. J. Heittokangas, "Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity", J. Math. Anal. Appl, 355(1), pp.352~363 (2009)
  7. I. Laine, "Clunie theorem for difference and q-difference polynomials", J. London. Math. Soc. (2), 76(3), pp.556~566 (2007)
  8. P. Li, "When an entire function and its linear differential polynomial share two values", Illinois J. Math, 44(2), pp.349~362 (2000)
  9. R. Nevanlinna, "Le theoreme de Picard-Borel et la theorie des fonctions meromorphes" (1929), Gauthiers-Villars
  10. C. C. Yang, "Uniqueness Theory of Meromorphic Functions" (2003), Kluwer Aca- demic Publishers
  11. J. L. Zhang, "On the Nevanlinna characteristic of f(qz) and its appli-cations", J. Math. Anal. Appl, 369(2), pp.537~544 (2010)

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