Hong-Xun Yi

Meromorphic functions that share one or two values

In this paper, we deal with the problem of uniqueness of meromorphic functions that share one or two values and obtain some results that are improvements of that of M. Ozawa, H. Ueda, G. Brosch, H. X. Yi and other authors. An example is provided to show that our results are sharp.

Unicity theorems for meromorphic or entire functions III

This paper studies the unique range set of meromorphic functions and shows that the set S = { w | w 13 + w 11 + 1 = 0} is unique range set of meromorphic functions with 13 elements.

Fixed-points and uniqueness of meromorphic functions

In the paper, we study the uniqueness and the shared fixed-points of meromorphic functions and prove two main theorems which improve the results of Fang and Fang and Qiu.

The unique range sets for entire or meromorphic functions

This paper studies the unique range sets of entire or meromorphic functions and shows that there exists a finite set Swith 13 elements such that for any two nonconstant meromorphic functions fand gthe condition Ef(S)= Eg(S)implies f≡ g. As a special case this also answers an open question posed by Gross about entire functions.

On a result of Singh

In this paper relations between T(r, f) and T(r, f (k) ) are established for a class of meromorphic functions f(z) , where T(r, f) and T(r, f (k) ) are the Nevanlinna characteristic functions f(z) and f (k) (z) respectively. An example is provided to show that a result of Singh is not true. The conclusions obtained here correct and generalise the result of Singh.

Uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a polynomial

In this paper, we get two uniqueness theorems of meromorphic functions whose certain nonlinear differential polynomials share a polynomial. The results in this paper extend the corresponding results given by Fang (2002) in [7]. Our reasoning in this paper will correct a defective reasoning in the proof of Theorem 4 in Bhoosnurmath and Dyavanal (2007) [8]. An example is provided to show that some conditions of the main results in this paper are necessary.

Some further results on uniqueness of meromorphic functions

This paper studies the problem of uniqueness of meromorphic functions and shows that there exists a set S with 11 elements such that any two nonconstant meromorphic functions f and g satisfying E3)(S,f) = E3)(S, g) must be identical, which improves a result of G. Frank and M. Reinders.

The reduced unique range sets for entire or meromorphic functions

This paper studies the reduced unique range sets of entire or meromorphic functions and exhibits a RURSE with 10 elemenis and aRURSM with 19 elemens.

Some further results on weighted sharing three values and Brosch's theorem

Using the notion of weighted sharing of values we prove two uniqueness theorems which improve the results proved by T.C. Alzahary [T.C. Alzahary, Weighted sharing three values and Broschs theorem. J. Math. Anal. Appl. 323 (2006) 8-25; T.C. Alzahary, On a result of Ueda concerning unicity of meromorphic functions. Kodai. Math. J. 30 (2007) 140-146], under a weaker hypothesis.

Meromorphic Functions Sharing a Nonzero Value with their Derivatives

Let f be a transcendental meromorphic function of nite order in the plane such that f (m) has nitely many zeros for some positive integer m ≥ 2: Suppose that f (k) and f share a CM, where k ≥ 1 is a positive integer, a 0 is a nite complex value. Then f is an entire function such that f (k) − a = c(f − a); where c 0 is a nonzero constant. The results in this paper are concerning a conjecture of Bruck (5). An example is provided to show that the results in this paper, in a sense, are the best possible.