The common value and uniqueness theorems of algebroid functions

Authors

  • Fujie Chai LMIB & School of Mathematics and Systems Science, Beihang University
  • Zongsheng Gao LMIB & School of Mathematics and Systems Science, Beihang University

DOI:

https://doi.org/10.14419/gjma.v3i1.4117

Keywords:

Algebroid functions, Common values, Growth, Uniqueness Theorems.

Abstract

In this paper, we investigate the common values and growth relationship between two algebroid functions and prove several growth theorems involving common values. Moreover, on this basis, we study uniqueness theory of algebroid function and prove several elegant uniqueness theorems.

References

[1] T.B. Cao, H.X. Yi, On the uniqueness theory of algebroid functions, Southeast Asian Bull. Math.}, Vol.33, No.1, (2009), pp. 25-39.

[2] F.J. Chai, The density of the common value-points of two algebroidal functions and the uniqueness theorems, Acta. Math. Sci., Vol.29A, No.6, (2009), pp. 1765-1770.

[3] W.K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, (1964).

[4] Y.Z. He, X.Z. Xiao, Algebroidal Functions and Ordinary Differential Equation, Sicence Press, Beijing, (1988).

[5] H.F. Liu, D.C. Sun, On the sharing values of algebroid functions and their derivatives, Acta. Math. Sci., Vol.33B, No.1, (2013), pp. 268-278.

[6] D.C. Sun, Z.S. Gao, Uniqueness theorem for algebroidal functions, J. South China Normal Univ., No.3,(2005), pp. 80-85.

[7] D.C. Sun, Z.S. Gao, Theorem for algebroidal functions, Acta Mathematica. Sinica., Vol.49, No.5, (2006), pp. 1027-1032.

[8] D.C. Sun, Z.S. Gao, Value Distribution of Algebroidal Functions, Sicence Press, Beijing, (2014).

[9] Z.X. Xuan, Z.S. Gao, Uniqueness theorem for algebroid functions, Complex Variables and Elliptic Equations., Vol.51, No.7, (2006), pp. 701-712.

[10]L. Yang, Value Distribution Theory and its New Reaserch, Springer-Verlag, Berlin Heidelberg, (1993).

[11]C.C. Yang, H.X. Yi, Uniqueness Theory for Meromorphic Functions, Kluwer Academic Publishers, Boston, (2003).

[12]X.M. Zhang, D.C. Sun, Uniqueness of algebroidal functions, Acta. Math. Sci., Vol.31A, No.4, (2011), pp. 1133-1139.

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Published

09-02-2015

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Section

Articles

How to Cite

Chai, F., & Gao, Z. (2015). The common value and uniqueness theorems of algebroid functions. Global Journal of Mathematical Analysis, 3(1), 26-32. https://doi.org/10.14419/gjma.v3i1.4117