Uniqueness of Meromorphic Functions with Their Nonlinear Differential Polynomials Share a Small Function

ABSTRACT

In this paper we deal with the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share a small function. We consider the case for some general differential polynomials [f^{n}P(f)f^{,}] where P(f) is a polynomial which generalize some result due to Abhijit Banerjee and Sonali Mukherjee [1].

In this paper we deal with the uniqueness of meromorphic functions when two nonlinear differential polynomials generated by two meromorphic functions share a small function. We consider the case for some general differential polynomials [f

Cite this paper

nullH. Waghamore and T. Adaviswamy, "Uniqueness of Meromorphic Functions with Their Nonlinear Differential Polynomials Share a Small Function,"*Applied Mathematics*, Vol. 2 No. 11, 2011, pp. 1364-1368. doi: 10.4236/am.2011.211191.

nullH. Waghamore and T. Adaviswamy, "Uniqueness of Meromorphic Functions with Their Nonlinear Differential Polynomials Share a Small Function,"

References

[1] A. Banerjee and S. Mukherjee, “Nonlinear Differential Polynomials Sharing a Small Function,” Archivum Mathematicum, Vol. 44, No. 1, 2008, pp. 41-56.

[2] L. Yang, “Value Distribution Theory,” Springer, Berlin, Germany, 1993.

[3] C.-Y. Fang and M.-L. Fang, “Uniqueness of Meromor-Phic Functions and Differential Polynomials,” Computers and Mathematics with Applications, Vol. 44, No. 5-6, 2002, pp. 607-617. doi:10.1016/S0898-1221(02)00175-X

[4] W.-C. Lin and H.-X. Yi, “Uniqueness Theorems for Meromorphic Functions,” Indian Journal of Pure and Applied Mathematics, Vol. 35, No. 2, 2004, pp. 121-132.

[5] W.-C. Lin and H.-X. Yi, “Uniqueness Theorems for Meromorphic Functions Concerning Fixed Points,” Complex Variables: Theory and Applications, Vol. 49, No. 11, 2004, pp. 793-806.

[6] A. Banerjee, “On Uniqueness for Nonlinear Differential Polynomials Sharing the Same 1-Point,” Annales Polonici Mathematici, Vol. 89, No. 3, 2006, pp. 259-272. doi:10.4064/ap89-3-3

[7] I. Lahiri and A. Sarkar, “Nonlinear Differential Polyno-Mials Sharing 1-Points with Weight Two,” Chinese Journal Contemporary Mathematics, Vol. 25, No. 3, 2004, pp. 325-334.

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

[9] H.-X. Yi, “Meromorphic Functions that Share One or Two Values,” Complex Variables: Theory and Applications, Vol. 28, No. 1. 1995, pp. 1-11.

[10] H.-X. Yi, “Uniqueness of Meromorphic Functions and a Question of C. C. Yang,” Complex Variables: Theory and Applications, Vol. 14, No. 14, 1990, pp. 169-176.

[1] A. Banerjee and S. Mukherjee, “Nonlinear Differential Polynomials Sharing a Small Function,” Archivum Mathematicum, Vol. 44, No. 1, 2008, pp. 41-56.

[2] L. Yang, “Value Distribution Theory,” Springer, Berlin, Germany, 1993.

[3] C.-Y. Fang and M.-L. Fang, “Uniqueness of Meromor-Phic Functions and Differential Polynomials,” Computers and Mathematics with Applications, Vol. 44, No. 5-6, 2002, pp. 607-617. doi:10.1016/S0898-1221(02)00175-X

[4] W.-C. Lin and H.-X. Yi, “Uniqueness Theorems for Meromorphic Functions,” Indian Journal of Pure and Applied Mathematics, Vol. 35, No. 2, 2004, pp. 121-132.

[5] W.-C. Lin and H.-X. Yi, “Uniqueness Theorems for Meromorphic Functions Concerning Fixed Points,” Complex Variables: Theory and Applications, Vol. 49, No. 11, 2004, pp. 793-806.

[6] A. Banerjee, “On Uniqueness for Nonlinear Differential Polynomials Sharing the Same 1-Point,” Annales Polonici Mathematici, Vol. 89, No. 3, 2006, pp. 259-272. doi:10.4064/ap89-3-3

[7] I. Lahiri and A. Sarkar, “Nonlinear Differential Polyno-Mials Sharing 1-Points with Weight Two,” Chinese Journal Contemporary Mathematics, Vol. 25, No. 3, 2004, pp. 325-334.

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

[9] H.-X. Yi, “Meromorphic Functions that Share One or Two Values,” Complex Variables: Theory and Applications, Vol. 28, No. 1. 1995, pp. 1-11.

[10] H.-X. Yi, “Uniqueness of Meromorphic Functions and a Question of C. C. Yang,” Complex Variables: Theory and Applications, Vol. 14, No. 14, 1990, pp. 169-176.