TITLE

# Meromorphic Functions Sharing a Small Function

AUTHOR(S)
Songmin Wang; Zongsheng Gao
PUB. DATE
January 2007
SOURCE
Abstract & Applied Analysis;2007, p1
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We will study meromorphic functions that share a small function, and prove the following result: let f (z) and g(z) be two transcendental meromorphic functions in the complex plane and let n â‰¥ 11 be a positive integer. Assume that a(z)(â‰¢ 0) is a common small function with respect to f (z) and g(z). If fn f' and gng' share a(z) CM, then either fn(z) f' (z)gn(z)g' (z) â‰¡ aÂ²(z), or f (z) â‰¡ tg(z) for a constant satisfying tn+1 = 1. As applications, we give several examples.
ACCESSION #
28138840

## Related Articles

• L1TV Computes the Flat Norm for Boundaries. Morgan, Simon P.; Vixie, Kevin R. // Abstract & Applied Analysis;2007, p1

We show that the recently introduced LÂ¹TV functional can be used to explicitly compute the flat norm for codimension one boundaries. Furthermore, using LÂ¹TV, we also obtain the flat norm decomposition. Conversely, using the flat norm as the precise generalization of LÂ¹TV functional, we...

• Monotonicity of a Key Function Arised in Studies of Nematic Liquid Crystal Polymers. Hongyun Wang; Hong Zhou // Abstract & Applied Analysis;2007, p1

We revisit a key function arised in studies of nematic liquid crystal polymers. Previously, it was conjectured that the function is strictly decreasing and the conjecture was numerically confirmed. Here we prove the conjecture analytically. More specifically, we write the derivative of the...

• Periodic Solutions to a Kind of Second Order Neutral Functional Differential Equation in the Critical Case. Shi Ping Lu; Wei Gao Ge; Zu Xiu Zheng // Acta Mathematica Sinica;Oct2005, Vol. 21 Issue 5, p1149

In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows: in the critical case | c| = 1. By employing Mawhin's continuation theorem and some analysis techniques, some new results are obtained.

• Analytic solutions of an iterative differential equation under Brjuno condition. Liu, Jian; Si, Jian // Acta Mathematica Sinica;Sep2009, Vol. 25 Issue 9, p1469

In this paper, the differential equation involving iterates of the unknown function, with a complex parameter a, is investigated in the complex field â„‚ for the existence of analytic solutions. First of all, we discuss the existence and the continuous dependence on the parameter a of...

• Admissible Solutions of the Schwarzian Type Difference Equation. Baoqin Chen; Sheng Li // Abstract & Applied Analysis;2014, p1

This paper is to investigate the Schwarzian type difference equation [(Î”Â³f/Î”f) - (3/2)(Î”Â²f/Î”)Â²]k = R(z, f) = (P(z, f)/Q(z, f)), where R(z, f) is a rational function in f with polynomial coefficients, P(z, f), respectively Q(z, f) are two irreducible polynomials in f of...

• Meromorphic Functions with Three Weighted Sharing Values. Xiao-Min Li; Hong-Xun Yi // Journal of Biology;2008, Vol. 8, p623

In this paper, we prove some results on uniqueness of meromorphic functions with three weighted sharing values. The results in this paper improve those given by H. X. Yi, I. Lahiri, T. C. Alzahary and H. X. Yi and other authors.

• THE $2\times 2$ SPECTRAL NEVANLINNAPICK PROBLEM. CONSTANTIN COSTARA // Journal of the London Mathematical Society;Jun2005, Vol. 71 Issue 3, p684

A method is presented to construct interpolation functions into the $2\times 2$ open spectral unit ball. For the spectral NevanlinnaPick problem, these functions are in some sense extremal, and the set of all these interpolation functions is enough to solve any interpolation problem, with...

• On unicity of meromorphic function and k-th derivative of its n-th power. Lahiri, Indrajit; Mandal, Nintu // Journal of Advanced Research in Applied Mathematics;2012, Vol. 4 Issue 3, p1

In this paper, we study the uniqueness problem for a meromorphic function and k-th order derivative of its n-th power. The result in this paper improves and supplements some previous results due to Meng [6], Lahiri and Sarkar [5], Yu [10], Zhang [11] and Zhang and Lu [13].

• Uniqueness and zeros of q-shift difference polynomials. LIU, KAI; LIU, XIN-LING; CAO, TING-BIN // Proceedings of the Indian Academy of Sciences: Mathematical Scie;Aug2011, Vol. 121 Issue 3, p301

In this paper, we consider the zero distributions of q-shift difference polynomials of meromorphic functions with zero order, and obtain two theorems that extend the classical Hayman results on the zeros of differential polynomials to q-shift difference polynomials. We also investigate the...

Share