Admissible Solutions of the Schwarzian Type Difference Equation
This paper is to investigate the Schwarzian type difference equation Δ3f/Δf-3/2Δ2f/Δf2k=Rz,f=P(z,f)/Q(z,f), where R(z,f) is a rational function in f with polynomial coefficients, P(z,f), respectively Q(z,f) are two irreducible polynomials in f of degree p, respectively q. Relationship between p and...
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| Format: | Article |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/306360 |
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| _version_ | 1849693468204466176 |
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| author | Baoqin Chen Sheng Li |
| author_facet | Baoqin Chen Sheng Li |
| author_sort | Baoqin Chen |
| collection | DOAJ |
| description | This paper is to investigate the Schwarzian type difference equation Δ3f/Δf-3/2Δ2f/Δf2k=Rz,f=P(z,f)/Q(z,f), where R(z,f) is a rational function in f with polynomial coefficients, P(z,f), respectively Q(z,f) are two irreducible polynomials in f of degree p, respectively q. Relationship between p and q is studied for some special case. Denote d=maxp,q. Let f(z) be an admissible solution of (*) such that ρ2(f)<1; then for s (≥2) distinct complex constants α1,…,αs , q+2k∑j=1sδ(αj,f)≤ 8k. In particular, if N(r,f)=S(r,f), then d+2k∑j=1sδ (αj,f)≤4k. |
| format | Article |
| id | doaj-art-2fbd57736e854919a7c490e8418e7237 |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2fbd57736e854919a7c490e8418e72372025-08-20T03:20:24ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/306360306360Admissible Solutions of the Schwarzian Type Difference EquationBaoqin Chen0Sheng Li1College of Science, Guangdong Ocean University, Zhanjiang 524088, ChinaCollege of Science, Guangdong Ocean University, Zhanjiang 524088, ChinaThis paper is to investigate the Schwarzian type difference equation Δ3f/Δf-3/2Δ2f/Δf2k=Rz,f=P(z,f)/Q(z,f), where R(z,f) is a rational function in f with polynomial coefficients, P(z,f), respectively Q(z,f) are two irreducible polynomials in f of degree p, respectively q. Relationship between p and q is studied for some special case. Denote d=maxp,q. Let f(z) be an admissible solution of (*) such that ρ2(f)<1; then for s (≥2) distinct complex constants α1,…,αs , q+2k∑j=1sδ(αj,f)≤ 8k. In particular, if N(r,f)=S(r,f), then d+2k∑j=1sδ (αj,f)≤4k.http://dx.doi.org/10.1155/2014/306360 |
| spellingShingle | Baoqin Chen Sheng Li Admissible Solutions of the Schwarzian Type Difference Equation Abstract and Applied Analysis |
| title | Admissible Solutions of the Schwarzian Type Difference Equation |
| title_full | Admissible Solutions of the Schwarzian Type Difference Equation |
| title_fullStr | Admissible Solutions of the Schwarzian Type Difference Equation |
| title_full_unstemmed | Admissible Solutions of the Schwarzian Type Difference Equation |
| title_short | Admissible Solutions of the Schwarzian Type Difference Equation |
| title_sort | admissible solutions of the schwarzian type difference equation |
| url | http://dx.doi.org/10.1155/2014/306360 |
| work_keys_str_mv | AT baoqinchen admissiblesolutionsoftheschwarziantypedifferenceequation AT shengli admissiblesolutionsoftheschwarziantypedifferenceequation |