Related papers: Meromorphic functions and linearization phenomena …

In [Israel J. Math, 2014], Grahl and Nevo obtained a significant improvement for the well-known normality criterion of Montel. They proved that for a family of meromorphic functions $\mathcal F$ in a domain $D\subset \mathbb C,$ and for a…

We consider the difference Schr{\''o}dinger equation $\psi(z+h)+\psi(z-h)+ v(z)\psi(z)=0$ where $z$ is a complex variable and $h$ is a small positive parameter. If $v$ is an analytic function, then, for $h$ sufficiently small, the analytic…

Let F and G be two families of meromorphic functions on a domain D, and let a, b and c be three distinct points in the extended complex plane. Let G be a normal family in D such that all limit functions of G are non-constant. If for each f…

The main purpose of this article is concerned with the existence and the precise forms of the transcendental solutions of several refined versions of Fermat-type functional equations with polynomial coefficients in several complex variables…

The purpose of this paper is to investigate the following invariance equation involving two $2$-variable generalized Bajraktarevi\'c means, i.e., we aim to solve the functional equation $$…

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 $k(\geq1)$…

We prove the meromorphy of solutions for a wide class of ordinary differential equations. These equations are given by invariant manifolds of non-linear partial differential equations integrable by the inverse scattering method. Some higher…

In this article we consider functions $f$ meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions. This condition simplifies and generalizes known conditions. We…

We introduce and develop the root locus method in mathematics. And we study the distribution of zeros of meromorphic functions by root locus method.

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…

In this research notes, we investigate some remain problems in the uniqueness of meromorphic function. Using some deep results of Yamanoii, we obtain some results in this notes.

Our aim in this paper is to prove, under some growth conditions on the datas, the solvability in a Gevrey class of a polynomially nonlinear functional differential equation.

The Schwarzian derivative plays a fundamental role in complex analysis, differential equations, and modular forms. In this paper, we investigate its higher-order generalizations, known as higher Schwarzians, and their connections to…

It is shown that if three distinct values of a meromorphic function f:C^n -> P^1 of hyper-order strictly less than 2/3 have forward invariant pre-images with respect to a translation t:C^n -> C^n, t(z)=z+c, then f is a periodic function…

We consider the $n{\times}n$ matrix linear differential systems in the complex plane. We find necessary and sufficient conditions under which these systems have meromorphic fundamental solutions. Using the operator identity method we…

A meromorphic function on a compact complex analytic manifold defines a $\bc\infty$ locally trivial fibration over the complement of a finite set in the projective line $\bc\bp^1$. We describe zeta-functions of local monodromies of this…

Uniform asymptotic formulae for arrays of complex numbers of the form $(f_{r,s})$, with $r$ and $s$ nonnegative integers, are provided as $r$ and $s$ converge to infinity at a comparable rate. Our analysis is restricted to the case in which…

For differential equations $P(y^{(k)},y)=0,$ where $P$ is a polynomial, we prove that all meromorphic solutions having at least one pole are elliptic functions, possibly degenerate.

The paper is devoted to study the uniqueness problem of linear delay-differential operator of a meromorphic function sharing two sets or small function together with values with its $c$-shift and $q$-shift operator. Results of this paper…

This paper is devoted to the investigation of multidimensional analogues of refined Bohr-type inequalities for bounded holomorphic mappings on the unit polydisc $\mathbb{P}\Delta(0;1_n)$. We provide a definitive resolution to the Bohr…