arXiv subjects

Mohamed Amine Zemirni

Publications and source records attributed to Mohamed Amine Zemirni.

4 recordsLinked to original sources

arXiv2025

Tumura-Clunie Differential Equations with Applications to Linear ODE's

In this paper, we study nonlinear differential equations of Tumura-Clunie type, $ f^n + P(z, f) = h, $ where $ n \geq 2 $ is an integer, $ P(z, f) $ is a differential polynomial in $ f $ of degree $ γ_P \leq n - 1 $ with small functions as coefficients, and $ h $ is a meromorphic function. Assuming that $ h $ satisfies a linear differential equation of order $ p\le n $ with rational coefficients, we establish a result that classifies the meromorphic solutions $ f $ into two cases based on the distribution of their zeros and poles. This result is then applied to study the zeros and critical points of entire solutions to certain higher-order linear differential equations, thereby extending some known results in the literature.

math.CV↗

arXiv2023

On Relative Convex Sequences

In this paper, we introduce the concept of relative convex sequences and establish their fundamental properties, highlighting their similarities to those of convex sequences. Additionally, we prove new inequalities of the Lupas and Hermite-Hadamard-Fejér type for relative convex sequences. In certain cases, and as an application, we show how the concept of relative convexity can facilitate the derivation of new inequalities for convex sequences.

math.CV↗

arXiv2022

New findings on the periodicity of entire functions and their differential polynomials

In this paper, we seek to explore under what conditions the periodicity of an entire function $ f(z) $ follows from the periodicity of a differential polynomial in $ f(z) $. We improve and generalize some earlier results and we give other new findings.

math.CV↗

arXiv2019

On meromorphic solutions of non-linear differential equations of Tumura-Clunie type

Meromorphic solutions of non-linear differential equations of the form $f^n+P(z,f)=h$ are investigated, where $n\geq 2$ is an integer, $h$ is a meromorphic function, and $P(z,f)$ is differential polynomial in $f$ and its derivatives with small functions as its coefficients. In the existing literature this equation has been studied in the case when $h$ has the particular form $h(z)=p_1(z)e^{α_1(z)}+p_2(z)e^{α_2(z)}$, where $p_1, p_2$ are small functions of $f$ and $α_1,α_2$ are entire functions. In such a case the order of $h$ is either a positive integer or equal to infinity. In this article it is assumed that $h$ is a meromorphic solution of the linear differential equation $h'' +r_1(z) h' +r_0(z) h=r_2(z)$ with rational coefficients $r_0,r_1,r_2$, and hence the order of $h$ is a rational number. Recent results by Liao-Yang-Zhang (2013) and Liao (2015) follow as special cases of the main results.

math.CV↗