Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their q-Shift
We investigate value distribution and uniqueness problems of meromorphic functions with their q-shift. We obtain that if f is a transcendental meromorphic (or entire) function of zero order, and Q(z) is a polynomial, then afn(qz)+f(z)−Q(z) has infinitely many zeros, where q∈ℂ∖{0}, a is nonzero const...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/818052 |
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| _version_ | 1832556075240390656 |
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| author | Haiwa Guan Gang Wang Qiuqin Luo |
| author_facet | Haiwa Guan Gang Wang Qiuqin Luo |
| author_sort | Haiwa Guan |
| collection | DOAJ |
| description | We investigate value distribution and uniqueness problems of meromorphic functions with their q-shift. We obtain that if f is a transcendental meromorphic (or entire) function of zero order, and Q(z) is a polynomial, then afn(qz)+f(z)−Q(z) has infinitely many zeros, where q∈ℂ∖{0}, a is nonzero constant, and n≥5 (or n≥3). We also obtain that zero-order meromorphic function share is three distinct values IM with its q-difference polynomial P(f), and if limsup r→∞(N(r,f)/T(r,f))<1, then f≡P(f). |
| format | Article |
| id | doaj-art-8b21a5291dc04ca79e53ed77ac376be8 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8b21a5291dc04ca79e53ed77ac376be82025-02-03T05:46:27ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/818052818052Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their q-ShiftHaiwa Guan0Gang Wang1Qiuqin Luo2Department of Public Teaching, Wenzhou Vocational College of Science and Technology, Zhejiang, Wenzhou 325000, ChinaDepartment of Science and Humanities, Shandong Transport Vocational College, Shandong, Weifang 261206, ChinaDepartment of Educational Administration and Supervision, Wenzhou Vocational College of Science and Technology, Zhejiang, Wenzhou 325000, ChinaWe investigate value distribution and uniqueness problems of meromorphic functions with their q-shift. We obtain that if f is a transcendental meromorphic (or entire) function of zero order, and Q(z) is a polynomial, then afn(qz)+f(z)−Q(z) has infinitely many zeros, where q∈ℂ∖{0}, a is nonzero constant, and n≥5 (or n≥3). We also obtain that zero-order meromorphic function share is three distinct values IM with its q-difference polynomial P(f), and if limsup r→∞(N(r,f)/T(r,f))<1, then f≡P(f).http://dx.doi.org/10.1155/2012/818052 |
| spellingShingle | Haiwa Guan Gang Wang Qiuqin Luo Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their q-Shift Discrete Dynamics in Nature and Society |
| title | Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their q-Shift |
| title_full | Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their q-Shift |
| title_fullStr | Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their q-Shift |
| title_full_unstemmed | Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their q-Shift |
| title_short | Value Distribution and Uniqueness Results of Zero-Order Meromorphic Functions to Their q-Shift |
| title_sort | value distribution and uniqueness results of zero order meromorphic functions to their q shift |
| url | http://dx.doi.org/10.1155/2012/818052 |
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