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...
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| Format: | Article |
| Language: | English |
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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 |
| _version_ | 1819160827238809600 |
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| author | Changjiang Song Kai Liu Lei Ma |
| author_facet | Changjiang Song Kai Liu Lei Ma |
| author_sort | Changjiang Song |
| collection | DOAJ |
| description | 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). |
| first_indexed | 2024-12-22T17:02:38Z |
| format | Article |
| id | doaj.art-65cda6e9b5b343cfa1744ae74f467716 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T17:02:38Z |
| publishDate | 2018-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-65cda6e9b5b343cfa1744ae74f4677162022-12-21T18:19:17ZengSpringerOpenAdvances in Difference Equations1687-18472018-07-012018111410.1186/s13662-018-1712-xThe zeros on complex differential-difference polynomials of certain typesChangjiang Song0Kai Liu1Lei Ma2Department of Mathematics, Nanchang UniversityDepartment of Mathematics, Nanchang UniversityDepartment of Mathematics, Nanchang UniversityAbstract 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).http://link.springer.com/article/10.1186/s13662-018-1712-xDifferential-difference polynomialsZerosFinite order |
| spellingShingle | Changjiang Song Kai Liu Lei Ma The zeros on complex differential-difference polynomials of certain types Advances in Difference Equations Differential-difference polynomials Zeros Finite order |
| title | The zeros on complex differential-difference polynomials of certain types |
| title_full | The zeros on complex differential-difference polynomials of certain types |
| title_fullStr | The zeros on complex differential-difference polynomials of certain types |
| title_full_unstemmed | The zeros on complex differential-difference polynomials of certain types |
| title_short | The zeros on complex differential-difference polynomials of certain types |
| title_sort | zeros on complex differential difference polynomials of certain types |
| topic | Differential-difference polynomials Zeros Finite order |
| url | http://link.springer.com/article/10.1186/s13662-018-1712-x |
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