Uniqueness of a meromorphic functions that share one small function and its derivative.

In this paper we consider the problem of uniqueness of meromorphic functions that share one small function and its derivatives, and obtain two theorems which improve the result of Qingcai Zhang [11]

On meromorphic functions that share a small function with its derivatives.

In this paper, we study the problem of meromorphi functions sharing a small function with its derivative and prove one theorem. The theorem improves the results of Jin-Dong Li and Guang-Xin Huang [10]

Weighted sharing of meromorphic functions concerning certain type of linear difference polynomials

In this research article, with the help of Nevanlinna theory we study the uniqueness problems of transcendental meromorphic functions having finite order in the complex plane $\mathbb{C}$, of the form is given by $\phi^{n}(z)\sum_{j=1}^{d}a_{j}\phi(z+c_{j})$ and $\psi^{n}(z)\sum_{j=1}^{d}a_{j}\psi(z+c_{j})$ where $L(z,\phi)=\sum_{j=1}^{d}a_{j}\phi(z+c_{j})$ which share a non-zero polynomial $p(z)$ with finite weight. By considering the concept of weighted sharing introduced by I. Lahiri (Complex Variables and Elliptic equations,2001,241-253), we investigate difference polynomials for the cases $(0,2),(0,1),(0,0)$. Our new findings extends and generalizes some classical results of Sujoy Majumder\cite{m11}. Some examples have been exhibited which are relevant to the content of the paper

Weighted sharing of meromorphic functions concerning certain type of linear difference polynomials

In this research article, with the help of Nevanlinna theory we study the uniqueness problems of transcendental meromorphic functions having finite order in the complex plane $\mathbb{C}$, of the form is given by $\phi^{n}(z)\sum_{j=1}^{d}a_{j}\phi(z+c_{j})$ and $\psi^{n}(z)\sum_{j=1}^{d}a_{j}\psi(z+c_{j})$ where $L(z,\phi)=\sum_{j=1}^{d}a_{j}\phi(z+c_{j})$ which share a non-zero polynomial $p(z)$ with finite weight. By considering the concept of weighted sharing introduced by I. Lahiri (Complex Variables and Elliptic equations,2001,241-253), we investigate difference polynomials for the cases $(0,2),(0,1),(0,0)$. Our new findings extends and generalizes some classical results of Sujoy Majumder\cite{m11}. Some examples have been exhibited which are relevant to the content of the paper

Generalization of Uniqueness of Meromorphic Functions Sharing Fixed Point

In this paper, we study the uniquenessproblems of entire and meromorphic functions concerning differentialpolynomials sharing fixed point and obtain some results which generalize theresults due to Subhas S. Bhoosnurmath and Veena L. Pujari [1]

Uniqueness of Meromorphic Functions of Differential Polynomials Sharing a Small Function with Finite Weight

Let f be a non-constant meromorphic function and a = a ( z ) {a=a(z)} ( 0 , ∞ {\not\equiv 0,\infty} ) a small function of f.Here, we obtain results similar to the results due to Indrajit Lahiri and Bipul Pal[Uniqueness of meromorphic functions with their homogeneous and linear differential polynomials sharing a small function,Bull. Korean Math. Soc. 54 2017, 3, 825–838]for a more general differential polynomial by introducing the concept of weighted sharing

Uniqueness of polynomial and differential monomial

In this paper, we discuss the problem of meromorphic functions sharing small function and present one theorem which extend a result of K. S. Charak and Banarasi Lal [16]

Generalization of uniqueness and value sharing of meromorphic functions concerning differential polynomials

The motivation of this paper is to study the uniqueness problems of meromorphic functions concerning differential polynomials that share a small function. The results of the paper improve and generalize the recent results due to Fengrong Zhang and Linlin Wu [13]. We also solve an open problem as posed in the last section of [13]

Fixed-Points and Uniqueness of Entire and Meromorphic Functions

In this paper, we deal with the uniqueness problems on entire and meromorphic functions concerning differential polynomials that share fixed-points. These results improve and extend those given by Xiaojuan Li and C. Meng, see [2