Difference Polynomials Of Meromorphic Functions Research Articles

Uniqueness of Differential Polynomials of Meromorphic Functions Sharing a Small Function Without Counting Multiplicity

Abstract The paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function without counting multiplicity. The results of this paper are extension of some problems studied by K. Boussaf et. al. in [2] and generalization of some results of S.S. Bhoosnurmath et. al. in [4].

Uniqueness of meromorphic functions sharing a value or small function

Abstract The paper concerns interesting problems related to the field of Complex Analysis, in particular Nevanlinna theory of meromorphic functions. The author have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a value or small function. The results of this paper are generalizations of some problems studied in [BOUSSAF, K.—ESCASSUT, A.—OJEDA, J.: Complex meromorphic functions f′P′(f), g′P′(g) sharing a small function, Indag. Math. (N.S.) 24 (2013), 15–41] and in [DYAVANAL, R. S.: Uniqueness and value-sharing of differential polynomials of meromorphic functions, J. Math. Anal. Appl. 374 (2011), 335–345].

Zeros and shared one value of q-shift difference polynomials

In this paper, we investigate uniqueness problems and zero distributions of q-shift difference polynomials of meromorphic functions with zero order in the complex plane. The obtained results extend some previous known results.

A note on value distribution of difference polynomials of meromorphic functions

In this paper, we investigate the value distribution of the difference counterpart Δf(z)-af(z)nof f′(z) -af(z)n and obtain an almost direct difference analogue of result of Hayman.

Differential polynomials sharing one value

In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k+12. If fn + af(k) and gn + ag(k) share b CM and the b-points of fn + af(k) are not the zeros of f and g, then f and g are either equal or closely related.

Nevanlinna Theory for the Uniqueness of Difference Polynomials and Meromorphic Functions by Sharing one Small Function

The purpose of this paper is to extend the usual Nevanlinna theory to the periodic functions, difference operators and difference polynomials of meromorphic functions concerning their uniqueness after sharing one small function and satisfying certain conditions on the number of zeros and poles of the functions.

Value distribution of certain difference polynomials of meromorphic functions

In this paper, we establish a theorem concerning value distribution of certain difference polynomials of meromorphic functions, which extends [{\bf14}, Theorem 2] and [{\bf16}, Theorem 1.2]. Applying this result, we prove some uniqueness theorems of meromorphic functions whose certain difference polynomials share a non-zero polynomial, which extends [{\bf18}, Theorems 1.1 and 1.2] and [{\bf23}, Theorem 6], where the meromorphic functions are of finite order.

Uniqueness of difference polynomials of meromorphic functions

In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.

Zeros and Uniqueness of Difference Polynomials of Meromorphic Functions

Zeros and Uniqueness of Difference Polynomials of Meromorphic Functions

Uniqueness of meromorphic functions sharing one small function

In this paper, we study the uniqueness problem of nonlinear differential polynomials of meromorphic functions that share one small function a(z). Our results extend the corresponding result obtained by Zhang et al. (2008).

On the value distribution and uniqueness of difference polynomials of meromorphic functions

In this paper, we study the zeros of difference polynomials of meromorphic functions of the forms

Value Sharing Results forq-Shifts Difference Polynomials

We investigate the zero distribution ofq-shift difference polynomials of meromorphic functions with zero order and obtain some results that extend previous results of K. Liu et al.

The Zeros of a Certain Homogeneous Difference Polynomials of Meromorphic Functions

Let f(z) be a function transcendental and meromorphic in the plane of growth order less than 1. This paper focuses on discuss and estimate the number of the zeros of a certain homogeneous difference polynomials of degree k in f(z), and obtains that this certain homogeneous difference polynomials has infinitely many zeros.

The zeros of q-shift difference polynomials of meromorphic functions

In this paper, we investigate the value distribution of difference polynomials and related to two well-known differential polynomials, where is a meromorphic function with finite logarithmic order. MSC:30D35, 39B12.

Value distribution of difference polynomials of meromorphic functions

We investigate the characteristic function and the zeros of difference polynomials. In particular, wepartly extend the Valiron-Mohon’ko theorem to difference polynomials and establish difference analogues of someclassical results about the zeros of differential polynomials.

The Zeros of Difference Polynomials of Meromorphic Functions

We investigate the value distributions of difference polynomials Δf(z) − af(z) n and f(z) nf(z + c) which related to two well‐known differential polynomials, where f(z) is a meromorphic function.

Some results about a special nonlinear difference equation and uniqueness of difference polynomial

In this paper, we continue to study a special nonlinear difference equation solutions of finite order entire function. We also continue to investigate the value distribution and uniqueness of difference polynomials of meromorphic functions. Our results which improve the results of Yang and Laine [Proc. Jpn. Acad. Ser. A Math. Sci. 83:50-55 (2007)]; Qi et al. [Comput. Math. Appl. 60:1739-1746 (2010) ].Mathematics Subject Classification (2000): 30D35, 39B32, 34M05.

Uniqueness and zeros of q-shift difference polynomials

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 uniqueness problem of q-shift difference polynomials that share a common value.

On properties of difference polynomials

We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f(z)f(z+c).

Value Distributions and Uniqueness of Difference Polynomials

We investigate the zeros distributions of difference polynomials of meromorphic functions, which can be viewed as the Hayman conjecture as introduced by (Hayman 1967) for difference. And we also study the uniqueness of difference polynomials of meromorphic functions sharing a common value, and obtain uniqueness theorems for difference.