SOME RESULTS ON THE QUESTIONS OF KIT-WING YU Majumder, Sujoy;
The paper deals with the problem of meromorphic functions sharing a small function with its differential polynomials and improves the results of Liu and Gu , Lahiri and Sarkar , Zhang  and Zhang and Yang  and also answer some open questions posed by Kit-Wing Yu . In this paper we provide some examples to show that the conditions in our results are the best possible.
uniqueness;meromorphic function;sharing small function;
R. Bruck, On entire functions which share one value CM with their first derivative, Results Math. 30 (1996), no. 1-2, 21-24.
G. G. Gundersen, Meromorphic functions that share finite values with their derivative, J. Math. Anal. Appl. 75 (1980), no. 2, 441-446.
G. G. Gundersen, Meromorphic functions that share two finite values with their derivative, Pacific J. Math. 105 (1983), no. 2, 299-309.
G. G. Gundersen and L. Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998), no. 1, 88-95.
I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206.
I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), no. 3, 241-253.
I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J. 26 (2003), no. 1, 95-100.
I. Lahiri and A. Sarkar, Uniqueness of a meromorphic function and its derivative, J. Inequal. Pure Appl. Math. 5 (2004), no. 1, Art. 20, 9 pp.
L. Liu and Y. Gu, Uniqueness of meromorphic functions that share one small function with their derivatives, Kodai Math. J. 27 (2004), no. 3, 272-279.
W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), no. 2-4, 195-206.
L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Lecture Notes in Math., Vol. 599, pp. 101-103, Springer-Verlag, New York, 1977.
Q. C. Zhang, Meromorphic function that share one small function with its derivative, J. Inequal. Pure Appl. Math. 6 (2005), no. 4, Art. 116, 13 pp.
J. L. Zhang and L. Z. Yang, Some results related to a conjecture of R. Bruck concerning meromorphic functions sharing one small function with their derivatives, Ann. Acad. Sci. Fenn. Math. 32 (2007), no. 1, 141-149.
C. C. Yang, On deficiencies of differential polynomials II, Math. Z. 125 (1972), 107-112.
K. W. Yu, On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4 (2003), no. 1, Art. 21, 7 pp.