Uniqueness of meromorphic functions concerning derivatives and fixed points

On the uniqueness of meromorphic functions that share four values in one angular domain

In this paper, we investigate the problem of uniqueness of a non-constant meromorphic function f and its differential polynomial Q[f] when they share two distinct, non-zero, small meromorphic function IM*, where we have taken the conditions N(r, f) = S(r, f) and N(r, 0, f) < λT(r, f), λ

In this article we investigate the uniqueness of transcendental meromorphic function dealing with four shared values in one angular domain instead of the whole complex plane.

In this paper we investigate the uniqueness of transcendental meromorphic function dealing with the shared values in some angular domains instead of the whole complex plane.

This article deals with problems of the uniqueness of transcendental meromorphic function with shared values in some angular domains dealing with the multiple values which improve a result of J. Zheng.

In this paper, we study the value distribution and the uniqueness of meromorphic function in Class A. We obtain significant result which improve as well as generalize the result of C.C.Yang and Xinhou Hua.

On the multiple values and uniqueness of meromorphic functions on annuli

Preface. 1: Nevanlinna theory. 1.1. Parabolic manifolds and Hermitian geometry. 1.2. The first main theorem. 1.3. Growths of meromorphic functions. 1.4. The lemma of logarithmic derivative. 1.5. Growth estimates of Wronskians. 1.6. The second main theorem. 1.7. Degenerate holomorphic curves. 1.8. Value distribution of differential polynomials. 1.9. The second main theorem for small functions. 1.10. Tumura-Clunie theory. 1.11. Generalizations of Nevanlinna theorem. 1.12. Generalizations of Borel theorem. 2: Uniqueness of meromorphic functions on C. 2.1. Functions that share four values. 2.2. Functions that share three values CM. 2.3. Functions that share pairs of values. 2.4. Functions that share four small functions. 2.5. Functions that share five small functions. 2.6. Uniqueness related to differential polynomials. 2.7. Polynomials that share a set. 2.8. Meromorphic functions that share the same sets. 2.9. Unique range sets. 2.10. Uniqueness polynomials. 3: Uniqueness of meromorphic functions on Cm. 3.1. Technical lemmas. 3.2. Multiple values of meromorphic functions. 3.3. Uniqueness of differential polynomials. 3.4. The four-value theorem. 3.5. The three-value theorem. 3.6. Generalizations of Rubel-Yang's theorem. 3.7. Meromorphic functions sharing one value. 3.8. Unique range sets of meromorphic functions. 3.9. Unique range sets ignoring multiplicities. 3.10. Meromorphic functions of order 4.8. Propagation theorems. 4.9. Uniqueness dealing with multiple values. 5: Algebroid functions of several variables. 5.1. Preliminaries. 5.2. Techniques of value distribution. 5.3. The second main theorem. 5.4. Algebroid reduction of meromorphic mappings. 5.5. The growth of branching divisors. 5.6. Reduction of Nevanlinna theory. 5.7. Generalizations of Malmquist theorem. 5.8. Uniqueness problems. 5.9. Multiple values of algebroid functions. References. Symbols. Index.

In this paper, we study the uniqueness problems on meromorphic function and its kth order derivative. The results in this paper improve the results given by K. W. Yu (On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4(1)(2003), Art. 21), L. P. Liu and Y. X. Gu (Uniqueness of meromorphic functions that share one small function with their derivatives, Kodai Math. J. 27(2004), 272-279) and supple- ment a result of S. H. Lin and W. C. Lin (Uniqueness of meromorphic functions concerning weakly weighted sharing, Kodai Math. J. 29(2006), 269-280).

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 [fnP(f)f,] where P(f) is a polynomial which generalize some result due to Abhijit Banerjee and Sonali Mukherjee [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 c1, c2, c, are three constants, satisfying (c1 c2)n+1c>n+1=- 1 or f = tg for a constant t such that tn+1 = 1

We prove that the Nevanlinna five-point-theorem on the uniqueness of meromorphic functions is valid for five small meromorphic functions.

The authors establish certain results concerning the generalized Hadamard products of certain meromorphic univalent functions with positive coefficients analagous to the results due to Choi et al. (J. Math. Anal. Appl. 199(1996), 495–501).

In this article, we study the unicity of meromorphic functions concerning small functions and derivatives-differences. The results obtained in this article extend and improve some results of Chen et al. [Uniqueness problems on difference operators of meromorphic functions] and Chen and Huang [Uniqueness of meromorphic functions concerning their derivatives and shifts with partially shared values].

We investigate the relationship between Borel directions and uniqueness of meromorphic functions and obtain some results of meromorphic functions sharing four distinct values IM and one set in an angular domain containing a Borel line. Our result is an improvement of a recent theorem given by Long and Wu (2012).