VALUE DISTRIBUTION OF DIFFERENCE OPERATOR ON MEROMORPHIC FUNCTIONS

Some results on value distribution of the difference operator

In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

Fixed Points of Difference Operator of Meromorphic Functions

Let f be a transcendental meromorphic function of order less than one. The authors prove that the exact difference Δf =(z+1)-f(z) has infinitely many fixed points, if a ∈ ℂ and ∞ are Borel exceptional values (or Nevanlinna deficiency values) of f. These results extend the related results obtained by Chen and Shon.

some results on value distribution of the difference operator

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

Uniqueness and value distribution for difference operators of meromorphic function

Uniqueness And Value Distribution Of Differences Of Meromorphic Functions∗

The purpose of the paper is to study the uniqueness problems of difference polynomials of meromorphic functions sharing a small function. The results of the paper improve and generalize the recent results due to Liu, et al. [11] and Liu, et al. [12].