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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 hyperplanes with truncated counting functions. Our results are improvements of the previous…

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

The purpose of this paper is to prove the finiteness theorems for meromorphic mappings of a complete connected K\"{a}hler manifold into projective space sharing few hyperplanes in subgeneral position without counting multiplicity, where all…

Complex Variables · Mathematics 2020-03-10 Thoan Pham Duc , Tuyen Nguyen Dang , Vangty Noulorvang

In this paper, we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces (totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex…

Complex Variables · Mathematics 2022-07-25 Jiaxing Huang , Tuen Wai Ng

This paper is devoted to the uniqueness problem of the power of a meromorphic function with its differential polynomial sharing a set. Our result will extend a number of results obtained in the theory of normal families. Some questions are…

Complex Variables · Mathematics 2022-09-15 Abhijit Banerjee , Bikash Chakraborty

Let $c\in \mathbb{C}^{m},$ $f:\mathbb{C}^{m}\rightarrow\mathbb{P}^{n}(\mathbb{C})$ be a linearly nondegenerate meromorphic mapping over the field $\mathcal{P}_{c}$ of $c$-periodic meromorphic functions in $\mathbb{C}^{m}$, and let $H_{j}$…

Complex Variables · Mathematics 2016-01-22 Tingbin Cao , Risto Korhonen

In this paper, we shall study the uniqueness problems on meromorphic functions sharing a polynomial. We give a complete answer to a problem posed by Fang Mingliang. Our results improve or generalize those given by Fang and Hua, Yang and…

Complex Variables · Mathematics 2012-04-20 Xiao-Bin Zhang , Jun-Feng Xu , Hong-Xun Yi

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 purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an L-function when certain differential polynomial generated by them sharing a one degree polynomial. The main…

Complex Variables · Mathematics 2020-08-24 Abhijit Banerjee , Saikat Bhattacharyya

In this article, we prove that there are at most two meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)\ (n\geqslant 2)$ sharing $2n+2$ hyperplanes in general position regardless of multiplicity, where all zeros with…

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

In the context of several complex variables, we investigate the uniqueness problem for a power of a meromorphic function that shares a value with its $k$-th order directional derivative in $\mathbb{C}^m$. Our results extend previous…

Complex Variables · Mathematics 2025-11-04 Abjijit Banerjee , Sujoy Majumder , Debabrata Pramanik

The purpose of this article has two fold. The first is to generalize some recent second main theorems for the mappings and moving hyperplanes of $\P^n(\C)$ to the case where the counting functions are truncated multiplicity (by level $n$)…

Complex Variables · Mathematics 2019-02-13 Duc Thoan Pham , Hai Nam Nguyen , Van An Nguyen

In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.

Complex Variables · Mathematics 2017-05-11 Abhijit Banerjee , Sujoy Majumder , Bikash Chakraborty

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 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

Let $ H_1,\dots,H_{2n+2}$ be \emph{generic} $(2n+2)$ hyperplanes in $\mathbb{P}^n.$ It is proved that if meromorphic maps $ f $ and $ g $ of $\mathbb{C}^m $ into $\mathbb{P}^n $ satisfy $ f^*(H_j)=g^*(H_j)$ $(1\leq j\leq 2n+2)$ and $ g $ is…

Complex Variables · Mathematics 2023-08-04 Kai Zhou

The purpose of the paper is to rectify a series of errors occurred in [2], [17], [20] for a particular situation. To get a fruitful solution and to overcome the issue, we introduce a new form of set sharing namely restricted set sharing,…

Complex Variables · Mathematics 2021-03-02 Abhijit Banerjee , Arpita Kundu

The main aim of this article is to give some sufficient conditions for a family of meromorphic mappings on a domain D in C^n into P^N(C) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving…

Complex Variables · Mathematics 2015-05-11 Gerd Dethloff , Thai Do Duc , Trang Pham Nguyen Thu

Let $M$ be a complete K\"{a}hler manifold, whose universal covering is biholomorphic to a ball $\mathbb B^m(R_0)$ in $\mathbb C^m$ ($0<R_0\le +\infty$). Our first aim in this paper is to study the algebraic dependence problem of…

Complex Variables · Mathematics 2022-06-01 Si Duc Quang

In the existing literature, many researchers consider the uniqueness of the power of a meromorphic function with its derivative counterpart share certain values or small functions. Here we consider the same problem under the aegis of a more…

Complex Variables · Mathematics 2018-01-17 Abhijit Banerjee , Bikash Chakraborty

We prove uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values at the spectrum, Clark measure or the spectrum…

Complex Variables · Mathematics 2025-02-19 Burak Hatinoğlu