The partially shared values and small functions for meromorphic functions in a k-punctured complex plane

The main aim of this article is to discuss the uniqueness of meromorphic functions partially sharing some values and small functions in a k-punctured complex planeO. We proved the following: Let f1, f2 be two admissible meromorphic functions inO and aj (j = 1,2,..., l) be l(= 5) distinct small functions with respect to f and g. If E (aj, O, f1). E (aj, O, f2) (j = 1,2,..., l) and lim inf r.+8 lj =1 N0(r, 1 f1-aj) lj =1 N0(r, 1 f2-aj) > 5/2l - 5 then f1 = f2. Our results are some improvements and extension of previous theorems given by Cao-Yi and Ge-Wu.