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In this paper, we mainly propose improvements of the logarithmic difference lemma for meromorphic functions in several complex variables, and then investigate meromorphic solutions of partial difference equations from the viewpoint of…

Complex Variables · Mathematics 2019-09-10 Tingbin Cao , Ling Xu

Let $f$ be a meromorphic function on the complex plane $\mathbb C$ with the maximum function of its modulus $M(r,f)$ on circles centered at zero of radius $r$. A number of classical, well-known and widely used results allow us to estimate…

Complex Variables · Mathematics 2021-04-16 B. N. Khabibullin

The concept of proximate order is widely used in the theories of entire, meromorphic, subharmonic and plurisubharmonic functions. We give a general interpretation of this concept as a proximate growth function relative to a model growth…

Complex Variables · Mathematics 2019-12-03 Bulat N. Khabibullin

In this paper, we study $q$-difference analogues of several central results in value distribution theory of several complex variables such as $q$-difference versions of the logarithmic derivative lemma, the second main theorem for…

Complex Variables · Mathematics 2020-11-25 Tingbin Cao , Risto Korhonen

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

We show that if a meromorphic function has a direct singularity over infinity, then the escaping set has an unbounded component and the intersection of the escaping set with the Julia set contains continua. This intersection has an…

Complex Variables · Mathematics 2008-09-28 Walter Bergweiler , Philip J. Rippon , Gwyneth M. Stallard

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

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

We study one variable meromorphic functions mapping a planar real algebraic set $A$ to another real algebraic set in the complex plane. By using the theory of Schwarz reflection functions, we show that for certain $A$, these meromorphic…

Complex Variables · Mathematics 2022-04-15 Tuen-Wai Ng , Xiao Yao

The main object of the present paper is to, introduce the. class of meromorphic univalent functions Involving! hypergeomatrc function .We obtain~ some interesting geometric properties according to coefficient inequality , growth and…

Complex Variables · Mathematics 2020-05-15 Mazin Sh. Mahmoud , Abdul Rahman S. Juma , Raheam A. Mansor Al-Saphory

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

A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…

Numerical Analysis · Mathematics 2007-05-23 Rafael G. Campos , Claudio Meneses

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 contribution we announce a complete classification and new exotic phenomena of the meromorphic structure of $\z$-functions associated to conic manifolds proved in \cite{KLP1}. In particular, we show that the meromorphic extensions…

Mathematical Physics · Physics 2009-01-22 Klaus Kirsten , Paul Loya , Jinsung Park

We define an analogue of the Baernstein star function for a meromorphic function f in several complex variables. This function is subharmonic on the upper half-plane and encodes some of the main functionals attached to f.We then…

Complex Variables · Mathematics 2017-02-01 Faruk Abi-Khuzam , Florian Bertrand , Giuseppe Della Sala

In this article, we deal with the order of growth of solutions of non-homogeneous linear differential-difference equation \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=F(z), \end{equation*} where $A_{ij},$ $F\left(…

Complex Variables · Mathematics 2021-06-02 Rachid Bellaama , Benharrat Belaïdi

A two-parameter characteristic of functions meromorphic on annuli is introduced and an extension of the Nevanlinna value distribution theory for such functions is proposed.

Complex Variables · Mathematics 2008-07-09 Andriy Kondratyuk

Our primary aim is to explore a sufficient condition for the class of meromorphically convex functions of order $\alpha$, where $0 \leq \alpha < 1$. The investigation will focus on studying a class of continuous functions defined on…

Complex Variables · Mathematics 2025-05-13 Vibhuti Arora , Vinayak M

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

Necessary conditions are obtained for certain types of rational delay differential equations to admit a non-rational meromorphic solution of hyper-order less than one. The equations obtained include delay Painlev\'e equations and equations…

Complex Variables · Mathematics 2016-02-29 Rod Halburd , Risto Korhonen