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Meromorphic Functions Sharing a Nonzero Polynomial IM

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We study the uniqueness of meromorphic functions concerning nonlinear differential polynomials sharing a nonzero polynomial IM. Though the main concern of the paper is to improve a recent result of the present author [12], as a consequence of the main result we also generalize two recent results of X. M. Li and L. Gao [11].

Abstract

We study the uniqueness of meromorphic functions concerning nonlinear differential polynomials sharing a nonzero polynomial IM. Though the main concern of the paper is to improve a recent result of the present author [12], as a consequence of the main result we also generalize two recent results of X. M. Li and L. Gao [11].

참고문헌 (17)

  1. T. C. Alzahary, "Weighted value sharing and a question of I. Lahiri", Complex Var. Theory Appl., 49, pp.1063~1078 (2004)
  2. A. Banerjee, "Meromorphic functions sharing one value", Int. J. Math. Math. Sci., 22, pp.3587~3598 (2005)
  3. W. Bergweiler, "On the derivative of meromorphic functions with multiple zeros", J. Math. Anal. Appl., 278, pp.285~292 (2003)
  4. M. L. Fang, "A note on a problem of Hayman", Analysis, 20, pp.45~49 (2000)
  5. M. L. Fang, "Meromorphic functions that share xed points", J. Math. Anal. Appl., 268, pp.426~439 (2002)
  6. W. K. Hayman, "Picard values of meromorphic Functions and their derivatives", Ann. of Math, 70, pp.9~42 (1959)
  7. W. K. Hayman, "Meromorphic Functions" (1964), The Clarendon Press
  8. I. Lahiri, "Weighted value sharing and uniqueness of meromorphic functions", Complex Var. Theory Appl., 46, pp.241~253 (2001)
  9. I. Lahiri, "Value distribution of certain di erential polynomials", Int. J. Math. Math. Sc., 28, pp.83~91 (2001)
  10. I. Lahiri, "On a question of Hong Xun Yi", Arch Math, 38, pp.119~128 (2002)
  11. Xiao-Min Li, "MEROMORPHIC FUNCTIONS SHARING A NONZERO POLYNOMIAL CM", 대한수학회보, 47(2), pp.319~339 (2010), 대한수학회
  12. P. Sahoo, "Uniqueness of meromorphic functions when two di erential polynomials share one value IM", Mat. Vesnik, 62, pp.169~182 (2010)
  13. C. C. Yang, "On de ciencies of di erential polynomials II", Math. Z., 125, pp.107~112 (1972)
  14. C. C. Yang, "Uniqueness and value sharing of meromorphic functions", Ann. Acad. Sci. Fenn. Math., 22, pp.395~406 (1997)
  15. L. Yang, "Value Distribution Theory" (1993), Springer- Verlag
  16. H. X. Yi, "Uniqueness Theory of Meromorphic Functions" (1995), Science Press
  17. Q. C. Zhang, "Meromorphic function that shares one small function with its derivative", J. Inequal. Pure Appl. Math., 6, pp.116~ (2005)

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