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Uniqueness Of Meromorphic Functions Sharing A Small Function With Their Differential Polynomials

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With the aid of weakly weighted sharing and a recently introduced sharing notion in [3] known as relaxed weighted sharing we investigate the uniqueness of meromorphic functions sharing a small function with its differential polynomials. Our results will improve and supplement all the results obtained by Zhang and Yang [17] as well as a substantial part of the results recently obtained by the present author [2] and thus provide a better answer to the questions posed by Yu [14] in this regard.

Abstract

With the aid of weakly weighted sharing and a recently introduced sharing notion in [3] known as relaxed weighted sharing we investigate the uniqueness of meromorphic functions sharing a small function with its differential polynomials. Our results will improve and supplement all the results obtained by Zhang and Yang [17] as well as a substantial part of the results recently obtained by the present author [2] and thus provide a better answer to the questions posed by Yu [14] in this regard.

참고문헌 (17)

  1. A. Banerjee, "Weighted sharing of a small function by a meromorphic function and its derivative", Comput. Math. Appl, 53(11), pp.1750~1761 (2007)
  2. A. Banerjee, "Uniqueness of meromorphic functions sharing a small function with their derivatives", Math. Vesnik, 60, pp.121~135 (2008)
  3. A. Banerjee, "Uniqueness of meromorphic functions concerning differential monomials sharing the same value", Bull. Math. Soc. Sci. Math, 50(3), pp.191~206 (2007)
  4. R. Br¨uck, "On entire functions which share one value CM with their first derivative", Results Math, 30, pp.21~24 (1996)
  5. W. K. Hayman, "Meromorphic Functions" (1964), The Clarendon Press
  6. I. Lahiri, "Weighted sharing and uniqueness of meromorphic functions", Nagoya Math. J, 161, pp.193~206 (2001)
  7. I. Lahiri, "Weighted value sharing and uniqueness of meromorphic functions", Complex Var. Theory Appl, 46, pp.241~253 (2001)
  8. Indrajit Lahiri, "Weighted Sharing of Two Sets", Kyungpook Mathematical Journal, 46(1), pp.79~87 (2006), 경북대학교 자연과학대학 수학과
  9. I. Lahiri, "Uniqueness of meromorphic function and its derivative", J. Inequal. Pure Appl. Math, 5(1) (2004)
  10. S. Lin, "Uniqueness of meromorphic functions concerning weakly weighted sharing", Kodai Math. J, 29, pp.269~280 (2006)
  11. L. Liu, "Uniqueness of meromorphic functions that share one small function with their derivatives", Kodai Math. J, 27, pp.272~279 (2004)
  12. A. Z. Mohon’ko, "On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions", Functional Analysis and Their Applications, 14, pp.83~87 (1971)
  13. H. X. Yi, "On characteristic function of a meromorphic function and its derivative", Indian J. Math, 33(2), pp.119~133 (1991)
  14. K. W. Yu, "On entire and meromorphic functions that share small functions with their derivatives", J. Inequal. Pure Appl. Math, 4(1) (2003)
  15. Q.C.Zhang, "Meromorphic function that shares one small function with its derivative", J. Inequal. Pure Appl. Math, 6(4) (2005)
  16. J. L. Zhang, "Some results related to a conjecture of R.Br¨uck concerning meromorphic functions sharing one small function with their derivatives", Ann. Acad. Sci. Fenn. Math, 32, pp.141~149 (2007)
  17. J. L. Zhang, "Some results related to a conjecture of R.Br¨uck", J. Inequal. Pure Appl. Math, 8(1), pp.11~ (2007)

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