Proceedings of the Japan Academy, Series A, Mathematical Sciences

Meromorphic solutions of functional equations with nonconstant coefficients

Ping Li and Chung-Chun Yang

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Abstract

We have continued, by utilizing Nevanlinna's value distribution theory, our previous studies on the existence or solvability of meromorphic solutions of functional equations with constant coefficients to that of similar types of functional equations with meromorphic (small functions) coefficients. The results obtained are relating to value sharing or unicity of meromorphic functions.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 82, Number 10 (2007), 183-186.

Dates
First available in Project Euclid: 30 December 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1167536396

Digital Object Identifier
doi:10.3792/pjaa.82.183

Mathematical Reviews number (MathSciNet)
MR2303356

Zentralblatt MATH identifier
1124.30010

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory 30D05: Functional equations in the complex domain, iteration and composition of analytic functions [See also 34Mxx, 37Fxx, 39-XX]

Keywords
value distribution theory functional equation admissible solution

Citation

Li, Ping; Yang, Chung-Chun. Meromorphic solutions of functional equations with nonconstant coefficients. Proc. Japan Acad. Ser. A Math. Sci. 82 (2007), no. 10, 183--186. doi:10.3792/pjaa.82.183. https://projecteuclid.org/euclid.pja/1167536396


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References

  • F. Gross, On the equation $f^{n}+g^{n}=1$, Bull. Amer. Math. Soc. 72 (1966), 86–88.
  • F. Gross, Factorization of meromorphic functions and some open problems, in Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), 51–67. Lecture Notes in Math., 599, Springer, Berlin.
  • F. Gross and C.-C. Yang, On preimage and range sets of meromorphic functions, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), no. 1, 17–20.
  • G. G. Gundersen and K. Tohge, Entire and meromorphic solutions of $f\sp 5+g\sp 5+h\sp 5=1$, in Symposium on Complex Differential and Functional Equations, Univ. Joensuu, Joensuu, 2004, 57–67.
  • W. K. Hayman, Meromorphic functions, Clarendon Press, Oxford, 1964.
  • P.-C. Hu, P. Li and and C.-C. Yang, Unicity of meromorphic mappings, Kluwer Acad. Publ., Dordrecht, 2003.
  • I. Laine, Nevanlinna theory and complex differential equations, de Gruyter, Berlin, 1993.
  • P. Li and C.-C. Yang, Some further results on the unique range sets of meromorphic functions, Kodai Math. J. 18 (1995), no. 3, 437–450.
  • P. Li and C.-C. Yang, Admissible solutions of functional equations of Diophantine type. (Preprint).
  • R. Nevanlinna, Einige Eindentigkeitssätze in der Theorie der Meromorphen Funktionen, Acta Math. 48(1926), 367–391.
  • C.-C. Yang, A generalization of a theorem of P. Montel on entire functions, Proc. Amer. Math. Soc. 26 (1970), 332–334.
  • C.-C. Yang and X.-H. Hua, Unique polynomials of entire and meromorphic functions, Mat. Fiz. Anal. Geom. 4 (1997), no. 3, 391–398.
  • C.-C. Yang and P. Li, Some further results on the functional equation $P(f)=Q(g)$, in Value distribution theory and related topics, Kluwer Acad. Publ., Boston, MA., 2004, 219–231.
  • H.-X. Yi, On a question of Gross, Sci. China Ser. A 38 (1995), no. 1, 8–16.