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In this paper, we study the uniqueness of the difference of meromorphic functions. We prove the following result: Let $f$ be a non-constant meromorphic function of hyper-order less than $1$, let $\eta$ be a non-zero complex number,…

Complex Variables · Mathematics 2023-08-09 XiaoHuang Huang

This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, studies an answer to a question posed by Gross for a particular class of meromorphic…

Complex Variables · Mathematics 2021-01-19 Bikash Chakraborty , Amit Kumar Pal , Sudip Saha , Jayanta Kamila

In the work, we focus on a conjecture due to Z.X. Chen and H.X. Yi[1] which is concerning the uniqueness problem of meromorphic functions share three distinct values with their difference operators. We prove that the conjecture is right for…

Complex Variables · Mathematics 2015-04-14 Feng Lü , Weiran Lü

In this paper, we prove some uniqueness results which improve and generalize several earlier works. Also, we prove a value distribution result concerning $f^{(k)}$ which provides a partial answer to a question of Fang and Wang [A note on…

Complex Variables · Mathematics 2014-12-30 Kuldeep Singh Charak , Banarsi Lal

In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].

Complex Variables · Mathematics 2015-07-31 Abdallah El Farissi , Zinelâabidine Latreuch , Benharrat Belaïdi , Asim Asiri

This paper has twofold. The first is to establish a second main theorem for meromorphic functions on the complex disc $\Delta (R_0)\subset\mathbb C$ with finite growth index and small functions, where the counting functions are truncated to…

Complex Variables · Mathematics 2024-03-26 Si Duc Quang

In this paper, we continue to investigate the uniqueness problem when an entire function $f$ and its linear differential polynomial $L(f)$ share two distinct complex values CMW (counting multiplicities in the weak sense) jointly. Also, We…

Complex Variables · Mathematics 2021-07-14 Goutam Haldar

The objective of the paper is twofold. The first objective is to study the uniqueness problem of meromorphic function $f(z)$ when $f^{(1)}(z)$ shares two distinct finite values $a_1$, $a_2$ and $\infty$ CM with $\Delta_cf(z)$. In this…

Complex Variables · Mathematics 2025-10-28 Abhijit Banerjee , Sujoy Majumder , Nabadwip Sarkar

An example in the article shows that the first derivative of $f(z)=\frac{2}{1-e^{-2z}}$ sharing $0$ CM and $1,\infty$ IM with its shift $\pi i$ cannot obtain they are equal. In this paper, we study the uniqueness of meromorphic function…

Complex Variables · Mathematics 2023-07-31 Xiao Huang

In this article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hypersurfaces with truncated counting functions. A uniqueness theorem for these mappings sharing…

Complex Variables · Mathematics 2014-09-19 Si Duc Quang

In this paper, we investigate the uniqueness problem of difference polynomials $f^{n}(z)P(f(z))L_c(f)$ and $g^{n}(z)P(g(z))L_c(g)$, where $L_c(f)=f(z+c)+c_0f(z)$, $P(z)$ is a polynomial with constant coefficients of degree $m$ sharing a…

Complex Variables · Mathematics 2021-03-19 Goutam Haldar

In this note, we introduce a new kind of pair of finite range sets in $\mathbb{C}$ for meromorphic functions corresponding to their uniqueness, i.e., how two meromorphic functions are uniquely determined by their two finite shared sets.

Complex Variables · Mathematics 2023-11-21 Amit Kumar Pal , Bikash Chakraborty , Sudip Saha

In this paper, we study the uniqueness of the differential-difference polynomials of entire functions on $\mathbb{C}^{n}$. We prove the following result: Let $f(z)$ be a transcendental entire function on $\mathbb{C}^{n}$ of hyper-order less…

Complex Variables · Mathematics 2021-06-07 Xiao Huang

In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two.

Complex Variables · Mathematics 2024-03-27 Sudip Saha , Amit Kumar Pal , Soumon Roy

In this paper, we study the uniqueness of the shift of meromorphic functions. We prove: Let $f$ be a non-constant meromorphic function satisfying $\rho_{2}(f)<1$, let $\eta$ be a non-zero complex number, and let $a,b,c\in\hat{S}(f)$ be…

Complex Variables · Mathematics 2024-01-18 XiaoHuang Huang

The purpose of the paper is to study the uniqueness problem of a $L$ function in the Selberg class sharing one or two sets with an arbitrary meromorphic function having finite poles. We manipulate the notion of weighted sharing of sets to…

Number Theory · Mathematics 2020-08-26 Abhijit Banerjee , Arpita Kundu

We prove some uniqueness results which improve and generalize results of Jiang-Tao Li and Ping Li[Uniqueness of entire functions concerning differential polynomials. Commun. Korean Math. Soc. 30 (2015), No. 2, pp. 93-101].

Complex Variables · Mathematics 2016-08-15 Kuldeep Singh Charak , Banarsi Lal

In this paper, we investigate meromorphic solutions in $\mathbb{C}^m$ of the nonlinear differential equation \[\displaystyle f^n\partial_u(f)g^n\partial_u(g)=1,\] where $\partial_u(f)=\sum_{j=1}^mu_j\partial_j(f)$ and $\sum_{j=1}^m u_j\neq…

Complex Variables · Mathematics 2025-11-14 Abhijit Banerjee , Sujoy Majumder , Debabrata Pramanik , Nabadwip Sarkar

The paper is devoted to study the uniqueness problem of linear delay-differential operator of a meromorphic function sharing two sets or small function together with values with its $c$-shift and $q$-shift operator. Results of this paper…

Complex Variables · Mathematics 2021-09-24 Arpita Roy , Abhijit Banerjee

This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set. Moreover, we will give the existence of unique range sets for meromorphic functions that are zero sets of polynomials that do not…

Complex Variables · Mathematics 2021-04-08 Bikash Chakraborty