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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/306360 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |