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UNIQUENESS OF ENTIRE FUNCTION SHARING TWO VALUES JOINTLY WITH ITS DIFFERENTIAL POLYNOMIALS

  • Goutam Haldar (Department of Mathematics, Ghani Khan Choudhury Institute of Engineering and Technology)
  • 투고 : 2023.12.26
  • 심사 : 2024.07.01
  • 발행 : 2024.12.20

초록

In this paper, we continue to investigate the uniqueness problem when an entire function f and its linear differential polynomial L(f) share two distinct complex values CMW (counting multiplicities in the weak sense) jointly. Also, We investigate the same problem when f and its differential monomial M(f) share two distinct complex values CMW, which is introduced by Lahiri in [Comput. Methods Funct. Theory, 21, 379-397 (2021)]. Our results generalize the recent result of Lahiri [Comput. Methods Funct. Theory, 21, 379-397 (2021)] to some extent.

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참고문헌

  1. G. Frank and W. Schwick, Meromorphie Funktionen, die mit einer Ableitung drei Werte teilen, Results Math. 22 (1992), 679-684. https://doi.org/10.1007/BF03323115
  2. G. Frank and X. Hua, Differential polynomials that share three values with their generated meromorphic function, Michigan Math. J. 46 (1999), no. 1, 175-186.
  3. Y. Gu, Uniqueness of an entire function and its differential polynomial, Acta Math. Sinica 37 (1994), no. 6, 791-798.
  4. G. G. Gundersen, Meromorphic functions that share finite values with their derivative, J. Math. Anal. Appl. 75 (1998), 441-446. https://doi.org/10.1016/0022-247X(80)90092-X
  5. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  6. I. Lahiri, An Entire Function Weakly Sharing a Doubleton with its Derivative, Comput. Methods Funct. Theory 21 (2021), 379-397. https://doi.org/10.1007/s40315-020-00355-4
  7. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, New York, 1993.
  8. P. Li, Value sharing and differential equations, J. Math. Anal. Appl. 310 (2005), 412-423. https://doi.org/10.1016/j.jmaa.2005.01.068
  9. P. Li and C. C. Yang, When an entire function and its linear differential polynomial share two values, Illinois J. Math. 44 (2000), no. 2, 349-362.
  10. P. Li and C. C. Yang, Value sharing of an entire function and its derivatives, J. Math. Soc. Japan. 51 (1999), no. 4, 781-799.
  11. A. Z. Mohon'ko, On the Nevanlinna characteristics of some meromorphic functions, Theory of Functions, Functional Analysis and Its Applications, Izd-vo Kharkovsk 14 (1971), 83-87.
  12. E. Mues and M. Reinders, Meromorphie Funktionen, die mit einem linearen Deerentialpolynom drei Werte teilen, Results Math. 22 (1992), 725-738. https://doi.org/10.1007/BF03323119
  13. E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), no. 2-4, 195-206. https://doi.org/10.1007/BF01303627
  14. L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivatives, Proc. Conf. Univ. of Kentucky, Lexington Ky, 1976, Lecture Notes in Math. 599 (1977), Berlin: Springer, 101-103.
  15. L. Z. Yang, Entire functions that share finite values with their derivatives, Bull. Aust. Math. Soc. 41 (1990), 337-342. https://doi.org/10.1017/S0004972700018190
  16. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht, 2003.