Uniqueness and Differential Polynomials of Meromorphic Functions

In this article, we study the uniqueness of Differential difference polynomials of L-function and Differential difference polynomials of a meromorphic function concerning weighted sharing of a polynomial. Our result improves and generalizes results of Abhijit Banerjee, Saikat Bhattacharyya [1], N. Mandal, N. K. Datta [5].

In this article, we study the uniqueness of Differential difference polynomials of L-function and Differential difference polynomials of a meromorphic function concerning weighted sharing of a polynomial. Our result improves and generalizes results of Abhijit Banerjee, Saikat Bhattacharyya [1], N. Mandal, N. K. Datta [5].

Off late, “Value Distribution Theory” concerning the differential polynomials of meromorphic functions is studied thoroughly. In this article, we consider a differential polynomial of a meromorphic function and its corresponding q-shift differential polynomial sharing the value 1, counted according to multiplicity and ignoring multiplicity to prove the uniqueness theorem. The concepts of normal families are employed to procure the main result, which in turn generalizes the existing result....

In this paper, we study the uniqueness of differential polynomials of meromorphic functions sharing one value, and obtain some results, which improve and generalize the related results due to Fang, Zhang-Lin, and Bhoosnurmath-Dyavanal, etc.

In this paper we discuss the uniqueness problem for differential and difference polynomials of the form (fnm(z)fnd(qz + c))(k) for meromorphic functions in a non-Archimedean field.

We prove the existance of a kind of singular directions concerning the differential polynomials\(f^{(k)} + \sum\limits_{j = 0}^{k - 1} {a_j f^{(j)} - af^n } \).

In the paper we study the uniqueness problem of certain differential polynomials generated by two meromorphic functions provided they share a small function along with some other conditions on the zeros and poles of the concerned functions.

Uniqueness and value-sharing of differential polynomials of meromorphic functions

In this paper, we investigate the uniqueness problem of meromorphic functions when nonlinear differential polynomials generated by them share a set of values with finite weight and obtain some results which generalize the results due to H.Y. Xu [J. Computational Analysis and Applications 16 (2014) 942-954].

Differential polynomials sharing one value

Uniqueness and value-sharing of differential polynomials of meromorphic functions

This research is a continuation of a recent paper, due to Liu and Laine, dealing with difference polynomials of entire function. In this paper, we investigate the value distribution of difference polynomials of meromorphic functions and prove some difference analogues to some classical results for differential polynomials.

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].

In this paper we prove the existence of singular point concerning differential polynomials of meromorphic functions with finite positive order.

The outcome of the research presented in this paper is the definition and investigation of two new subclasses of meromorphic functions. The new subclasses are introduced using a differential operator defined considering second-order differential polynomials of meromorphic functions in U\{0}=z∈C:0<z<1. The investigation of the two new subclasses leads to establishing inclusion relations and the proof of convexity and convolution properties regarding each of the two subclasses. Further, involving the concept of subordination, the Fekete–Szegö problem is also discussed for the aforementioned subclasses. Symmetry properties derive from the use of the convolution and from the convexity proved for the new subclasses of functions.