Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON THE UNIQUENESS OF CERTAIN TYPE OF SHIFT POLYNOMIALS SHARING A SMALL FUNCTION

  • Saha, Biswajit (Department of Mathematics Govt. General Degree College Muragachha)
  • Received : 2020.09.29
  • Accepted : 2020.10.28
  • Published : 2020.12.30
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Abstract

In this article, we consider the uniqueness problem of the shift polynomials $f^n(z)(f^m(z)-1){\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$ and $f^n(z)(f(z)-1)^m{\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$, where f(z) is a transcendental entire function of finite order, cj (j = 1, 2, …, s) are distinct finite complex numbers and n(≥ 1), m(≥ 1), s and µj (j = 1, 2, …, s) are integers. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo [Commun. Math. Stat. 3 (2015), 227-238].

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Acknowledgement

The author is grateful to the referees for reading the manuscript carefully and making a number of valuable comments and suggestions for the improvement of the paper.

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Cited by

  1. Weakly weighted sharing and unicity of certain shift polynomials vol.1978, pp.1, 2020, https://doi.org/10.1088/1742-6596/1978/1/012037