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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

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 investigate the uniqueness property of meromorphic functions together with its linear difference polynomial sharing two sets. Using the polynomial introduced in [FILOMAT 33(18)(2019), 6055-6072], we have improved the…

Complex Variables · Mathematics 2020-09-29 Goutam Haldar

The existence of meromorphic solutions to various difference equations has been extensively studied in recent years, the precise functional forms of such solutions -- particularly when the function and its difference operators share values…

Complex Variables · Mathematics 2026-04-17 Molla Basir Ahamed , Vasudevarao Allu

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

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

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

The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated. The $\varphi$-order is used as a general growth indicator, which covers the growth spectrum between the…

Complex Variables · Mathematics 2021-01-29 Hui Yu , Janne Heittokangas , Jun Wang , Zhi-Tao Wen

The paper gives a precise asymptotic relation between higher order logarithmic difference and logarithmic derivatives for meromorphic functions with order strictly less then one. This allows us to formulate a useful Wiman-Valiron type…

Complex Variables · Mathematics 2016-05-02 Yik-Man Chiang , Shao-Ji Feng

In this paper we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations with entire or meromorphic coefficients. We further extend and improve few results on the order of meromorphic…

Complex Variables · Mathematics 2022-06-23 Subhadip Khan , Chinmay Ghosh , Sanjib Kumar Datta

Let $f$ be a transcendental meromorphic function defined in the complex plane $\mathbb{C}$. We consider the value distribution of the differential polynomial $f^{q_{0}}(f^{(k)})^{q_{k}}$, where $q_{0}(\geq 2), q_{k}(\geq 1)$ are $k(\geq1)$…

Complex Variables · Mathematics 2020-01-07 Bikash Chakraborty , Sudip Saha , Amit Kumar Pal , Jayanta Kamila

In this paper, we investigate meromorphic solutions of certain nonlinear partial differential equations in several complex variables involving differential and functional operators. Let $f$ be a non-constant meromorphic function in…

Complex Variables · Mathematics 2026-05-11 Sujoy Majumder , Debabrata Pramanik , Jhilik Banerjee

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 article, we construct explicit meromorphic solutions of first order linear $q$-difference equations in the complex domain and we describe the location of all their zeros and poles. The homogeneous case leans on the study of four…

Complex Variables · Mathematics 2023-07-04 Alberto Lastra , Pascal Remy

Starting with a question of Yuan-Li-Yi [Value distribution of L-functions and uniqueness questions of F. Gross, Lithuanian Math. J., 58(2)(2018), 249-262] we have studied the uniqueness of a meromorphic function f and an L-function L…

Number Theory · Mathematics 2020-08-28 Abhijit Banerjee , Arpita Kundu

In this paper, we investigate shared value problems for shifts and higher-order difference operators of meromorphic and entire functions in several complex variables. Using Nevanlinna theory in $\mathbb{C}^n$, we obtain new uniqueness…

Complex Variables · Mathematics 2026-02-17 Abhijit Banerjee , Sujoy Majumder , Jhilik Banerjee

In this paper we prove the existence of meromorphic solutions to a nonlinear differential difference equation that describe certain self-similar potentials for the Schroedinger operator.

Mathematical Physics · Physics 2009-11-07 Alexander Tovbis

We consider a family of solutions of $q-$difference Riccati equation, and prove the meromorphic solutions of $q-$difference Riccati equation and corresponding second order $q-$difference equation are concerning with $q-$gamma function. The…

Complex Variables · Mathematics 2017-10-05 Zhibo Huang , Ranran Zhang

In this paper, we have investigated the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing a small function. Our results radically extended and improved the results of Bhoosnurmath-Pujari and…

Complex Variables · Mathematics 2019-07-01 Molla Basir Ahamed

This paper is devoted to investigate the singular directions of mero- morphic functions in some angular domains. We will confirm the existence of Hayman T directions in some angular domains. This is a continuous work of Yang [Yang L., Borel…

Complex Variables · Mathematics 2009-05-13 Wu Nan , Xuan Zuxing