Home Uniqueness of meromorphic functions sharing a value or small function
Article
Licensed
Unlicensed Requires Authentication

Uniqueness of meromorphic functions sharing a value or small function

  • Nguyen Van Thin EMAIL logo and Ha Tran Phuong
Published/Copyright: November 3, 2016
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 4

Abstract

The paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a value or small function. The results of this paper are generalizations of some problems studied in [BOUSSAF, K.—ESCASSUT, A.—OJEDA, J.: Complex meromorphic functionsf′P′(f), g′P′(g)sharing a small function, Indag. Math. (N.S.) 24 (2013), 15–41] and in [DYAVANAL, R. S.: Uniqueness and value-sharing of differential polynomials of meromorphic functions, J. Math. Anal. Appl. 374 (2011), 335–345].

Keywords: uniqueness theorem; differential polynomials
MSC 2010: Primary 30D35

(Communicated by Stanisława Kanas)

acknowledgement

The authors wish to thank the managing editor and referees for their very helpful comments and useful suggestions.

References

[1] An, T. T. H.—Wang, J. T. Y.—Wong, P. M.: Strong uniqueness polynomials: the complex case, Complex Var. Theory Appl. 49 (2004), 25–54.10.1080/02781070310001634601Search in Google Scholar

[2] Banerjee, A.—Bhattacharjee, P.: A uniqueness result related to certain non-linear differential polynomials sharing the same 1-points, Math. Slovaca 61 (2011), 181–196.10.2478/s12175-011-0004-7Search in Google Scholar

[3] Boussaf, K.—Escassut, A.—Ojeda, J.: Complex meromorphic functions f′P′(f), g′P′(g) sharing a small function, Indag. Math. (N.S.) 24 (2013), 15–41.10.1016/j.indag.2012.06.003Search in Google Scholar

[4] Dyavanal, R. S.: Uniqueness and value-sharing of differential polynomials of meromorphic functions, J. Math. Anal. Appl. 374 (2011), 335–345.10.1016/j.jmaa.2010.09.002Search in Google Scholar

[5] Escassut, A.: Meromorphic functions of uniqueness, Bull. Sci. Math. 131 (2007), 219–241.10.1016/j.bulsci.2006.05.004Search in Google Scholar

[6] Escassut, A.—Haddad, L.—Vidal, R.: URS and URSIM and non URS, J. Number Theory 75 (1999), 133–144.10.1006/jnth.1998.2324Search in Google Scholar

[7] Fujimoto, H.: On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122 (2000), 1175–1203.10.1007/978-1-4613-0269-8_34Search in Google Scholar

[8] Frank, G.—Reinders, M.: A unique range set for meromorphic functions with 11 elements, Complex Var. Theory. Appl. 37 (1998), 185–193.10.1080/17476939808815132Search in Google Scholar

[9] Li, P.—Yang, C. C.: Some further results on the unique range sets of meromorphic functions, Kodai Math. J. 18 (1995), 473–450.10.2996/kmj/1138043482Search in Google Scholar

[10] Lin, W.—Yi, H.: Uniqueness theorems for meromorphic functions concerning fixed-points, Complex Var. Theory Appl. 49 (2004), 793–806.10.1080/02781070412331298624Search in Google Scholar

[11] Lin, W.—Yi, H.: Uniqueness theorems for meromorphic functions, Indian J. Pure Appl. Math. 35 (2004), 121–132.Search in Google Scholar

[12] Yang, C. C.—Hua, X. H.: Uniqueness and value sharing of meromorphic function, Ann. Acad. Sci. Fenn. Math. 202 (1997), 395–406.Search in Google Scholar

[13] Zhang, X. Y.—Chen, J. F.—Lin, W. C.: Entire or meromorphic functions sharing one value, Comput. Math. Appl. 56 (2008), 1876–1883.10.1016/j.camwa.2008.04.008Search in Google Scholar

[14] Wang, L.—Luo, X.: Uniqueness of meromorphic functions concerning fixed points, Math. Slovaca 62 (2012), 29–38.10.2478/s12175-011-0069-3Search in Google Scholar

Received: 2013-11-29
Accepted: 2014-1-28
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Research Article
  2. Effect algebras with a full set of states
  3. Research Article
  4. An approach to orthomodular lattices via lattices with an antitone involution
  5. Research Article
  6. On properties of the free BCI-algebra with one generator
  7. Research Article
  8. The generalized order-k Narayana's cows numbers
  9. Research Article
  10. The irrationality of infinite series of a special kind
  11. Research Article
  12. On skew-commuting mappings in semiprime rings
  13. Research Article
  14. On the subordination and superordination of strongly starlike functions
  15. Research Article
  16. On a subclass of analytic functions involving Sălăgean integral operator
  17. Research Article
  18. Uniqueness of meromorphic functions sharing a value or small function
  19. Research Article
  20. A new inclusion for Bavrin's families of holomorphic functions in n-circular domains
  21. Research Article
  22. Oscillation of nonlinear fourth order mixed neutral differential equations
  23. Research Article
  24. Oscillation results for third order nonlinear mixed neutral differential equations
  25. Research Article
  26. Homoclinic solutions for second order Hamiltonian systems with general potentials
  27. Research Article
  28. A class of fractional impulsive functional differential equations with nonlocal conditions
  29. Research Article
  30. The weighted reverse poincaré type inequality for the difference of two parabolic subsolutions
  31. Research Article
  32. On the well posed solutions for nonlinear second order neutral difference equations
  33. Research Article
  34. Some approximation results for operators of Szász-Mirakjan-Durrmeyer type
  35. Research Article
  36. On the geometry of conditional expectations treated as projections on the L2-space
  37. Research Article
  38. Spectral problems of nonself-adjoint singular discrete Sturm-Liouville operators
  39. Research Article
  40. A necessary condition for the Smith equivalence of G-modules and its sufficiency
  41. Research Article
  42. On the internal approach to differential equations. 1. The involutiveness and standard basis
  43. Research Article
  44. Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three
https://doi.org/10.1515/ms-2015-0186
Keywords for this article
uniqueness theorem; differential polynomials

Articles in the same Issue

  1. Research Article
  2. Effect algebras with a full set of states
  3. Research Article
  4. An approach to orthomodular lattices via lattices with an antitone involution
  5. Research Article
  6. On properties of the free BCI-algebra with one generator
  7. Research Article
  8. The generalized order-k Narayana's cows numbers
  9. Research Article
  10. The irrationality of infinite series of a special kind
  11. Research Article
  12. On skew-commuting mappings in semiprime rings
  13. Research Article
  14. On the subordination and superordination of strongly starlike functions
  15. Research Article
  16. On a subclass of analytic functions involving Sălăgean integral operator
  17. Research Article
  18. Uniqueness of meromorphic functions sharing a value or small function
  19. Research Article
  20. A new inclusion for Bavrin's families of holomorphic functions in n-circular domains
  21. Research Article
  22. Oscillation of nonlinear fourth order mixed neutral differential equations
  23. Research Article
  24. Oscillation results for third order nonlinear mixed neutral differential equations
  25. Research Article
  26. Homoclinic solutions for second order Hamiltonian systems with general potentials
  27. Research Article
  28. A class of fractional impulsive functional differential equations with nonlocal conditions
  29. Research Article
  30. The weighted reverse poincaré type inequality for the difference of two parabolic subsolutions
  31. Research Article
  32. On the well posed solutions for nonlinear second order neutral difference equations
  33. Research Article
  34. Some approximation results for operators of Szász-Mirakjan-Durrmeyer type
  35. Research Article
  36. On the geometry of conditional expectations treated as projections on the L2-space
  37. Research Article
  38. Spectral problems of nonself-adjoint singular discrete Sturm-Liouville operators
  39. Research Article
  40. A necessary condition for the Smith equivalence of G-modules and its sufficiency
  41. Research Article
  42. On the internal approach to differential equations. 1. The involutiveness and standard basis
  43. Research Article
  44. Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 23.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2015-0186/html
Scroll to top button