Uniqueness Theorems on Difference Monomials of Entire Functions
The aim of this paper is to discuss the uniqueness of the difference monomials fnf(z+c). It assumed that f and g are transcendental entire functions with finite order and Ek)(1,fnf(z+c))=Ek)(1,gng(z+c)), where c is a nonzero complex constant and n, k are integers. It is proved that if one of the fol...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/407351 |
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| author | Gang Wang Deng-li Han Zhi-Tao Wen |
| author_facet | Gang Wang Deng-li Han Zhi-Tao Wen |
| author_sort | Gang Wang |
| collection | DOAJ |
| description | The aim of this paper is to discuss the uniqueness of the difference monomials fnf(z+c). It assumed that f and g are transcendental entire functions with finite order and Ek)(1,fnf(z+c))=Ek)(1,gng(z+c)), where c is a nonzero complex constant and n, k are integers. It is proved that if one of the following holds (i) n≥6 and k=3, (ii) n≥7 and k=2, and (iii) n≥10 and k=1, then fg=t1 or f=t2g for some constants t2 and t3 which satisfy t2n+1=1 and t3n+1=1. It is an improvement of the result of Qi, Yang and Liu. |
| format | Article |
| id | doaj-art-42361ea216ed4e58a9828c3a73e7f908 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-42361ea216ed4e58a9828c3a73e7f9082025-02-03T01:23:37ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/407351407351Uniqueness Theorems on Difference Monomials of Entire FunctionsGang Wang0Deng-li Han1Zhi-Tao Wen2Shandong Transport Vocational College, Weifang, Shandong 261206, ChinaLaiwu Vocational and Technical College, Laiwu, Shandong 271100, ChinaDepartment of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101 Joensuu, FinlandThe aim of this paper is to discuss the uniqueness of the difference monomials fnf(z+c). It assumed that f and g are transcendental entire functions with finite order and Ek)(1,fnf(z+c))=Ek)(1,gng(z+c)), where c is a nonzero complex constant and n, k are integers. It is proved that if one of the following holds (i) n≥6 and k=3, (ii) n≥7 and k=2, and (iii) n≥10 and k=1, then fg=t1 or f=t2g for some constants t2 and t3 which satisfy t2n+1=1 and t3n+1=1. It is an improvement of the result of Qi, Yang and Liu.http://dx.doi.org/10.1155/2012/407351 |
| spellingShingle | Gang Wang Deng-li Han Zhi-Tao Wen Uniqueness Theorems on Difference Monomials of Entire Functions Abstract and Applied Analysis |
| title | Uniqueness Theorems on Difference Monomials of Entire Functions |
| title_full | Uniqueness Theorems on Difference Monomials of Entire Functions |
| title_fullStr | Uniqueness Theorems on Difference Monomials of Entire Functions |
| title_full_unstemmed | Uniqueness Theorems on Difference Monomials of Entire Functions |
| title_short | Uniqueness Theorems on Difference Monomials of Entire Functions |
| title_sort | uniqueness theorems on difference monomials of entire functions |
| url | http://dx.doi.org/10.1155/2012/407351 |
| work_keys_str_mv | AT gangwang uniquenesstheoremsondifferencemonomialsofentirefunctions AT denglihan uniquenesstheoremsondifferencemonomialsofentirefunctions AT zhitaowen uniquenesstheoremsondifferencemonomialsofentirefunctions |