Uniqueness of Meromorphic Functions Concerning Differential Monomials

ABSTRACT

Considering the uniqueness of meromorphic functions concerning differential monomials ,we obtain that, if two non-constant meromorphic functions f(z) and g(z) satisfy ,where k and n are tow positive integers satisfying k ≥ 3 and n ≥ 11 , then either where c_{1}, c_{2}, c, are three constants, satisfying (c_{1} c_{2})^{n+1}c>^{n+1}=- 1 or f = tg for a constant t such that t^{n+1} = 1

Considering the uniqueness of meromorphic functions concerning differential monomials ,we obtain that, if two non-constant meromorphic functions f(z) and g(z) satisfy ,where k and n are tow positive integers satisfying k ≥ 3 and n ≥ 11 , then either where c

Cite this paper

nullH. Huang and B. Huang, "Uniqueness of Meromorphic Functions Concerning Differential Monomials,"*Applied Mathematics*, Vol. 2 No. 2, 2011, pp. 230-235. doi: 10.4236/am.2011.22025.

nullH. Huang and B. Huang, "Uniqueness of Meromorphic Functions Concerning Differential Monomials,"

References

[1] L. Yang, “Value Distribution Theory,” Springer-Verlag, Berlin, 1993.

[2] Y. F. Wang and M. L. Fang, “Picard Values and Normal Families of Meromorphic Functions with Multiple Zeros,” Acta Mathematica Sinica (N.S), Vol. 14, No. 1, 1998, pp. 17-26.

[3] H. H. Chen, “Yosida Function and Picard Values of Integral Functions and Their Derivatives,” Bulletin of the Australian Mathematical Society, Vol. 54, 1996, pp. 373-381. doi:10.1017/S000497270002178X

[4] M. L. Fang, “Uniqueness and Value-Sharing of Entire Functions,” Computers & Mathematics with Applications, Vol. 44, 2002, pp. 823-831. doi:10.1016/S0898-1221(02) 00194-3

[5] S. S. Bhoosnurmath and R. S. Dyavanal, “Uniqueness and Value-Sharing of Meromorphic Functions,” Applied mathematics, Vol. 53, 2007, pp. 1191-1205.

[6] C. C. Yang and X. H. Hua, “Uniqueness and Value-Sharing of Meromorphic Functions,” Annales Academi? Scientiarum Fennic? Mathematica, Vol. 22 , No. 2, 1997, p. 395.

[7] C. C. Yang, “On Deficiencies of Differential Polynomials,” Mathematische Zeitschrift, Vol. 125, No. 2, 1972, pp. 107-112. doi:10.1007/BF01110921

[8] H. X. Yi and C. C. Yang, “Uniqueness Theory of Meromorphic Functions,” Science Press, Beijing, 1995.

[9] C. Y. Fang and M. L. Fang, “Uniqueness Theory of Meromorphic Functions and Differential Polynomials,” Computers and Mathematics with Applications, Vol. 44, 2002, pp. 607-617. doi:10.1016/S0898-1221(02)00175-X

[1] L. Yang, “Value Distribution Theory,” Springer-Verlag, Berlin, 1993.

[2] Y. F. Wang and M. L. Fang, “Picard Values and Normal Families of Meromorphic Functions with Multiple Zeros,” Acta Mathematica Sinica (N.S), Vol. 14, No. 1, 1998, pp. 17-26.

[3] H. H. Chen, “Yosida Function and Picard Values of Integral Functions and Their Derivatives,” Bulletin of the Australian Mathematical Society, Vol. 54, 1996, pp. 373-381. doi:10.1017/S000497270002178X

[4] M. L. Fang, “Uniqueness and Value-Sharing of Entire Functions,” Computers & Mathematics with Applications, Vol. 44, 2002, pp. 823-831. doi:10.1016/S0898-1221(02) 00194-3

[5] S. S. Bhoosnurmath and R. S. Dyavanal, “Uniqueness and Value-Sharing of Meromorphic Functions,” Applied mathematics, Vol. 53, 2007, pp. 1191-1205.

[6] C. C. Yang and X. H. Hua, “Uniqueness and Value-Sharing of Meromorphic Functions,” Annales Academi? Scientiarum Fennic? Mathematica, Vol. 22 , No. 2, 1997, p. 395.

[7] C. C. Yang, “On Deficiencies of Differential Polynomials,” Mathematische Zeitschrift, Vol. 125, No. 2, 1972, pp. 107-112. doi:10.1007/BF01110921

[8] H. X. Yi and C. C. Yang, “Uniqueness Theory of Meromorphic Functions,” Science Press, Beijing, 1995.

[9] C. Y. Fang and M. L. Fang, “Uniqueness Theory of Meromorphic Functions and Differential Polynomials,” Computers and Mathematics with Applications, Vol. 44, 2002, pp. 607-617. doi:10.1016/S0898-1221(02)00175-X