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In the paper, we investigate the uniqueness problem of entire functions concerning their linear differential polynomial in shift and obtain three results which improve and generalize the recent result due to Qi (Ann. Polon. Math., 102…

Complex Variables · Mathematics 2025-12-03 Jeet Sarkar , Debabrata Pramanik

In this article, by introducing a new method in estimating the counting function of the auxiliary function, we prove a new generalization of uniqueness theorems for meromorphic mappings into $\P^n(\C )$ which share few hyperplanes…

Complex Variables · Mathematics 2019-02-27 Si Duc Quang

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

We consider the zeros distributions on the derivatives of difference polynomials of meromorphic functions, and present some results which can be seen as the discrete analogues of Hayman conjecture \cite{hayman1}, also partly answer the…

Complex Variables · Mathematics 2011-07-06 Kai Liu , Xin-Ling Liu , Ting-Bin Cao

We prove a new bound on the number of shared values of distinct meromorphic functions on a compact Riemann surface, explain a mistake in a previous paper on this topic, and give a survey of related questions.

Complex Variables · Mathematics 2022-06-08 Zhiguo Ding , Michael E. Zieve

We consider uniqueness results for meromorphic functions $f:{\mathbb C} \to \widehat{\mathbb C}$ such that for certain values $a\in {\mathbb C}$ the implication $f(z)=a \Rightarrow f'(z)=a$ holds, i.e. that $f$ and $f'$ share values {\it…

Complex Variables · Mathematics 2026-04-08 Andreas Sauer , Andreas Schweizer

Let f be a non-constant meromorphic function and a = a(z) be a small function of f. Under certain essential conditions, we obtained similar type conclusion of Bruck Conjecture, when f and its differential polynomial P[f] shares a with…

Complex Variables · Mathematics 2022-09-14 Bikash Chakraborty

Let f be a non constant meromorphic function and a(not identically zero or infinity) be a meromorphic function satisfying T(r,a) = o(T(r,f)) as r tends to infinity, and p(z) be a polynomial of degree n greater than or equal to 1 with p(0) =…

Complex Variables · Mathematics 2015-02-10 Kuldeep Singh Charak , Banarsi Lal

The subject of our thesis is the uniqueness theory of meromorphic functions and it is devoted to problems concerning Bruck conjecture, set sharing and related topics. The tool, we used in our discussions is classical Nevanlinna theory of…

Complex Variables · Mathematics 2017-11-27 Bikash Chakraborty

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

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 2022-05-09 XiaoHuang Huang

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 this article is to deal with the multiple values and uniqueness problem of meromorphic mappings from $\mathbb{C}^{m}$ into the complex projective space $\mathbb{P}^{n}(\mathbb{C})$ sharing fixed and moving hypersurfaces. We…

Complex Variables · Mathematics 2017-02-24 Tingbin Cao , Hongzhe Cao

In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the weaker hypothesis that the logarithmic derivative has finite lower order.

Complex Variables · Mathematics 2018-07-26 J. K. Langley

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

n this article we consider functions meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions which also contains some known results. We include few open problems for…

Complex Variables · Mathematics 2019-05-07 See Keong Lee , Saminathan Ponnusamy , Karl-Joachim Wirths

In this paper, we prove normality criteria for families of meromorphic functions involving sharing of a holomorphic function by a certain class of differential polynomials. Results in this paper extends the works of different authors…

Complex Variables · Mathematics 2015-04-01 Virender Singh , Kuldeep Singh Charak

In this paper, we investigate the zero distributions of $q$-shift difference-differential polynomials of meromorphic functions with zero-order that extends and generalizes the classical Hayman results of the zeros of differential…

Complex Variables · Mathematics 2021-03-09 Goutam Haldar

The $\varphi$-order was introduced in 2009 for meromorphic functions in the unit disc, and was used as a growth indicator for solutions of linear differential equations. In this paper, the properties of meromorphic functions in the complex…

Complex Variables · Mathematics 2020-10-26 Janne Heittokangas , Jun Wang , Zhi-Tao Wen , Hui Yu

The object of the present paper is to obtain a more general condition for univalence of meromorphic functions in the U*. The significant relationships and relevance with other results are also given. A number of known univalent conditions…

Complex Variables · Mathematics 2015-09-21 Erhan Deníz , Halit Orhan