• Title, Summary, Keyword: uniqueness theorems

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Weighted Value Sharing and Uniqueness of Entire Functions

  • Sahoo, Pulak
    • Kyungpook Mathematical Journal
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    • v.51 no.2
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    • pp.145-164
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    • 2011
  • In the paper, we study with weighted sharing method the uniqueness of entire functions concerning nonlinear differential polynomials sharing one value and prove two uniqueness theorems, first one of which generalizes some recent results in [10] and [16]. Our second theorem will supplement a result in [17].

MEROMORPHIC FUNCTIONS SHARING FOUR VALUES WITH THEIR DIFFERENCE OPERATORS OR SHIFTS

  • Li, Xiao-Min;Yi, Hong-Xun
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1213-1235
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    • 2016
  • We prove a uniqueness theorem of nonconstant meromorphic functions sharing three distinct values IM and a fourth value CM with their shifts, and prove a uniqueness theorem of nonconstant entire functions sharing two distinct small functions IM with their shifts, which respectively improve Corollary 3.3(a) and Corollary 2.2(a) from [12], where the meromorphic functions and the entire functions are of hyper order less than 1. An example is provided to show that the above results are the best possible. We also prove two uniqueness theorems of nonconstant meromorphic functions sharing four distinct values with their difference operators.

RESULTS ON MEROMORPHIC FUNCTIONS SHARING THREE VALUES WITH THEIR DIFFERENCE OPERATORS

  • LI, XIAO-MIN;YI, HONG-XUN;KANG, CONG-YUN
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1401-1422
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    • 2015
  • Under the restriction of finite order, we prove two uniqueness theorems of nonconstant meromorphic functions sharing three values with their difference operators, which are counterparts of Theorem 2.1 in [6] for a finite-order meromorphic function and its shift operator.

Some Further Results on Weighted Sharing of Values for Meromorphic Functions Concerning a Result of Terglane

  • Li, Xiao-Min;Yi, Hong-Xun
    • Kyungpook Mathematical Journal
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    • v.48 no.3
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    • pp.419-431
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    • 2008
  • In this paper, we deal with the problem of meromorphic functions that have three weighted sharing values, and obtain some uniqueness theorems which improve those given by N. Terglane, Hong-Xun Yi & Xiao-Min Li, and others. Some examples are provided to show that the results in this paper are best possible.

ON PARTIAL VALUE SHARING RESULTS OF MEROMORPHIC FUNCTIONS WITH THEIR SHIFTS AND ITS APPLICATIONS

  • Noulorvang, Vangty;Pham, Duc Thoan
    • Bulletin of the Korean Mathematical Society
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    • v.57 no.5
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    • pp.1083-1094
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    • 2020
  • In this paper, we give some uniqueness theorems of nonconstant meromorphic functions of hyper-order less than one sharing partially three or four small periodic functions with their shifts. As an application, some sufficient conditions for periodicity of meromorphic functions are given. Our results improve and extend previous results of W. Lin, X. Lin and A. Wu [11].