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On the meromorphic solutions of some functional equations

Published online by Cambridge University Press:  17 April 2009

Jianhua Chen
Affiliation:
Institute of Mathematics Huaibei Coal Industry Teachers College Huaibei, Anhui ProvincePeople's Republic of China
Jianyong Qiao
Affiliation:
Institute of Mathematics Fudan UniversityShanghaiPeople's Republic of China
Wenjun Zhang
Affiliation:
Institute of Mathematics Huaibei Coal Industry Teachers College Huaibei, Anhui Province
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Abstract

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Let f(z) be a meromorphic function, let P(z) and Q(z) be two polynomials. We shall investigate the asymptotic behaviour of the ratio T(r, f(P))/T(r, f(Q)), and discuss the growth of the meromorphic solutions of some functional equations.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Clunie, J., ‘The composition of entire and meromorphic function’, in Mathematical Essays Dedicated to A.J. Mclntyre (Ohio University Press, Athens, Ohio, 1970), pp. 7592.Google Scholar
[2]Korevaar, J., Entire functions and related parts of analysis, Proceedings of symposia in pure mathematics XI (Amer. Math. Soc., 1968).CrossRefGoogle Scholar
[3]Niino, K. and Suita, N., ‘Growth of a composite function of entire functions’, Kodai Math. J. 3 (1980), 374379.CrossRefGoogle Scholar
[4]Qiao, J., ‘On the growth of compositions of linear and meromorphic functions’, Bull. Austral. Math. Soc. 44 (1991), 263269.CrossRefGoogle Scholar
[5]Shimomura, S., ‘Entire solutions of a polynomial difference equation’, J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 28 (1981), 253266.Google Scholar
[6]Valiron, G., ‘Sur la dérivée des fonctoions algébroïdes’, Bull. Soc. Math. France 59 (1931), 1739.CrossRefGoogle Scholar
[7]Yanagihara, N., ‘Meromorphic solutions of some difference equations’, Funkcial Ekva. 23 (1980), 309326.Google Scholar
[8]Yanagihara, N., ‘Meromorphic solutions of some functional equations’, Bull. Sci. Math. 107 (1983), 289300.Google Scholar