The zeros on complex differential-difference polynomials of certain types
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2018-07-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1712-x |
| Summary: | 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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| ISSN: | 1687-1847 |