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Zayid Abdulhadi

Publications and source records attributed to Zayid Abdulhadi.

5 recordsLinked to original sources
arXiv2022

On the Bohr's inequality for stable mappings

We consider the class of \emph{stable} harmonic mappings $f=h+\overline{g}$ introduced by Martin, Hernandez, and the class of \emph{stable} logharmonic mappings $f=zh\overline{g}$ introduced by AbdulHadi, El-Hajj. We determine Bohr's radius for the classes of stable univalent harmonic mappings, stable convex harmonic mappings and stable univalent logharmonic mappings. We also consider improved and refined versions of Bohr's inequality and discuss the Bohr's Rogonsiski radius for these family of mappings.

math.CV↗
arXiv2020

On the univalence of polyanalytic functions

A continuous complex-valued function $F$ in a domain $D\subseteq\mathbf{C}$ is Poly-analytic of order $α$ if it satisfies $\partial^α_{\overline{z}}F=0.$ One can show that $F$ has the form $F(z)={\displaystyle\sum\limits_{0}^{n-1}}\overline{z}^{k}A_{k}(z)$, where each $A_k$ is an analytic function$.$ In this paper, we prove the existence of a Landau constant for Poly-analytic functions and the special Bi-analytic case. We also establish the Bohr's inequality for poly-analytic and bi-analytic functions which map $U$ into $U$. In addition, we give an estimate for the arclength over the class of poly-analytic mappings and consider the problem of minimizing moments of order $p$.

math.CV↗
arXiv2017

Characterizing Rotationally Typically Real Logharmonic Mappings

This paper treats the class of normalized logharmonic mappings f(z) = zh(z)bar{g(z)} in the unit disk satisfying ϕ(z) = zh(z)g(z) is analytically typically real. Every such mapping f is shown to be a product of two particular logharmonic mappings, each of which admits an integral representation. Also obtained is the radius of starlikeness and an upper estimate for arclength. Additionally, it is shown that f maps the unit disk into a domain symmetric with respect to the real axis when it is univalent and its second dilatation has real coefficients.

math.CV↗
arXiv2016

On geometrical properties of logharmonic mappings

In this paper, we find the radius of the disk $Ω_{r}$ such that every starlike logharmonic mapping $f(z)$ of order $α,$ is starlike in $% |z|\leq r$ with respect to any point of $Ω_{r}.$ We also establish a relation between the set of starlike logharmonic mappings \ and the set of starlike logharmonic mappings of order alpha. Moreover, the radius of starlikeness and univalence for the set of close to starlike logharmonic mappings of order $α$ is determined.

math.CV↗