Advances in Difference Equations (Jul 2018)

The zeros on complex differential-difference polynomials of certain types

  • Changjiang Song,
  • Kai Liu,
  • Lei Ma

DOI
https://doi.org/10.1186/s13662-018-1712-x
Journal volume & issue
Vol. 2018, no. 1
pp. 1 – 14

Abstract

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Abstract In this paper, we consider the zeros distribution of f(z)P(z,f)−q(z) $f(z)P(z,f) -q(z)$, where P(z,f) $P(z,f)$ is a linear differential-difference polynomial of a finite-order transcendental entire function f(z) $f(z)$, and q(z) $q(z)$ is a nonzero polynomial. To a certain extent, Theorem 1.1 generalizes the recent results (Latreuch and Belaïdi in Arab. J. Math. 7(1):27–37, 2018; Lü et al. in Kodai Math. J. 39(3):500–509, 2016) related to Hayman conjecture (Hayamn in Ann. Math. 70:9–42, 1959).

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