English
Related papers

Related papers: When a meromorphic function that omits three value…

200 papers

The main result of the paper determines all real meromorphic functions of finite order in the plane for which the first derivative has finitely many zeros, while the function itself and one of its higher derivatives have finitely many…

Complex Variables · Mathematics 2009-03-16 J. K. Langley

We investigate the existence and distribution of Herman rings of transcendental meromorphic functions which have at least one omitted value. If all the poles of such a function are multiple then it has no Herman ring. Herman rings of period…

Dynamical Systems · Mathematics 2015-01-08 Tarakanta Nayak

Our paper focuses on investigating the existence and possible forms of solutions to the nonlinear differential equation \beas f^m+\big(Rf^{(k)}\big)^n=Qe^{\alpha},\eeas where where $k$, $m$ and $n$ are three positive integers, $Q$ and $R$…

Complex Variables · Mathematics 2025-12-19 Sujoy majumder , Nabadwip Sarkar , Debabrata pramanik

In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…

Complex Variables · Mathematics 2018-01-08 Abhijit Banerjee , Bikash Chakraborty

We discuss meromorphic functions on the complex plane which are Brody curves regarded as holomorphic maps to P_1, i.e., which have bounded spherical derivative.

Complex Variables · Mathematics 2007-09-26 Joerg Winkelmann

In this paper, we have investigated the sufficient conditions for periodicity of meromorphic functions and obtained two results directly improving the result of \emph{Bhoosnurmath-Kabbur} \cite{Bho & Kab-2013}, \emph{Qi-Dou-Yang} \cite{Qi &…

Complex Variables · Mathematics 2018-04-03 M. B. Ahamed

We define the class of Left Located Divisor (LLD) meromorphic functions and their vertical order $m_0(f)$ and their convergence exponent $d(f)$. When $m_0(f)\leq d(f)$ we prove that their Weierstrass genus is minimal. This explains the…

Complex Variables · Mathematics 2013-06-11 Vicente Muñoz , Ricardo Pérez Marco

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

We show that for a vanishing period difference operator of a meromorphic function \( f \), there exist the following estimates regarding proximity functions, \[ \lim_{\eta \to 0} m_\eta\left(r, \frac{\Delta_\eta f - a\eta}{f' - a} \right) =…

Complex Variables · Mathematics 2025-05-28 Lasse Asikainen , Yu Chen , Risto Korhonen

Let $\Omega$ be a connected bounded domain on the complex plane, $S$ be its boundary, which is closed, star-shaped, $C^1$-smooth, and $H(\Omega)$ is the set of analytic (holomorphic) in $\Omega$ functions. The aim of this paper is to prove…

Complex Variables · Mathematics 2022-10-06 Alexander G. Ramm

In this paper we extend the concept of bi-univalent to the class of meromorphic functions. We propose to investigate the coefficient estimates for two classes of meromorphic bi-univalent functions. Also, we find estimates on the…

Complex Variables · Mathematics 2013-09-03 H. Orhan , N. Magesh , V. K. Balaji

If $f$ is a meromorphic function from the complex plane ${\mathbb C}$ to the extended complex plane $\overline{ {\mathbb C} }$, for $r > 0$ let $n(r)$ be the maximum number of solutions in $\{z\colon |z| \leq r \}$ of $f(z) = a$ for $a \in…

Complex Variables · Mathematics 2024-01-26 Aimo Hinkkanen , Joseph Miles

In this article, we study the growth of meromorphic solutions of linear delay-differential equation of the form \begin{equation*} \sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}(z)f^{(j)}(z+c_{i})=F(z), \end{equation*}% where $A_{ij}(z)$ $(i=0,1,\ldots…

Complex Variables · Mathematics 2022-12-27 Abdelkader Dahmani , Benharrat Belaïdi

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

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

A function which is transcendental and meromorphic in the plane has at least two singular values. On one hand, if a meromorphic function has exactly two singular values, it is known that the Hausdorff dimension of the escaping set can only…

Dynamical Systems · Mathematics 2023-04-18 Magnus Aspenberg , Weiwei Cui

A real arithmetic function f is multiplicatively monotonous if f (mn) -- f (m) has constant sign for m, n positive integers. Properties and examples of such functions are discussed, with applications to positive hermitian…

Number Theory · Mathematics 2018-09-25 Michel Balazard

The object of this paper is studying some properties of meromorphic functions which satisfy in the condition \[Re(zf(z)) > \alpha|z^2f'(z)+zf(z)| .\] Parallel results for some related classes are also obtained.

Complex Variables · Mathematics 2009-03-06 R. Aghalary , A. Ebadian , M. Eshaghi Gordji

The maximum of the modulus of a meromorphic function cannot be restricted from above by the Nevanlinna characteristic of this meromorphic function. But integrals from the logarithm of the module of a meromorphic function allow similar…

Complex Variables · Mathematics 2021-01-05 B. N. Khabibullin

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