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On the uniqueness of meromorphic function and its shift sharing values with truncated multiplicities

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In this paper, we deal with unicity of a nonconstant zero-order meromorphic function $f(z)$ and its shift $f(qz)$ when they share four distinct values $IM$ or share three distinct values with multiplicities truncated to level 4 in the extended complex plane, where $q\in\mathbb C\setminus\{0\}$. We also give an uniqueness result for $f(z)$ sharing sets with its shift.

Abstract

In this paper, we deal with unicity of a nonconstant zero-order meromorphic function $f(z)$ and its shift $f(qz)$ when they share four distinct values $IM$ or share three distinct values with multiplicities truncated to level 4 in the extended complex plane, where $q\in\mathbb C\setminus\{0\}$. We also give an uniqueness result for $f(z)$ sharing sets with its shift.

참고문헌 (14)

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  4. J. Heittokangas, "Uniqueness of meromorphic functions sharing values with their shifts", Complex Var. Elliptic Equ, 56(1-4), pp.81~92 (2011)
  5. J. Heittokangas, "Value sharing results for shifts of meromorphic functions, and sucient conditions for periodicity", J. Math. Anal. Appl, 355(1), pp.352~363 (2009)
  6. Xiao-Min Li, "Meromorphic functions sharing four values with their difference operators or shifts", 대한수학회보, 53(4), pp.1213~1235 (2016), 대한수학회
  7. Van An Nguyen, "Two meromorphic functions sharing four pairs of small functions", 대한수학회보, 54(4), pp.1159~1171 (2017), 대한수학회
  8. Xiaoguang Qi, "Value sharing results of a meromorphic function f(z) and f(qz)", 대한수학회보, 48(6), pp.1235~1243 (2011), 대한수학회
  9. X. Qi, "Sharing sets of q-dierence of meromorphic functions", Math. Slovaca, 64(1), pp.51~60 (2014)
  10. M. Ru, "Nevanlinna Theory and Its Relation to Diophantine Approximation" (2001), World Scientic Publishing Co., Inc.
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  12. C.-C. Yang, "Uniqueness Theory of Meromorphic Functions" (2003), Kluwer Academic Publishers Group
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  14. J. Zhang, "On the Nevanlinna characteristic of f(qz) and its applica-tions", J. Math. Anal. Appl, 369(2), pp.537~544 (2010)

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