On the Bohr's inequality for stable mappings
Zayid Abdulhadi, Layan El Hajj
TL;DR
This paper investigates Bohr's inequality for various classes of stable harmonic and logharmonic mappings, determining their Bohr radii and exploring refined inequalities and related radii.
Contribution
It establishes Bohr's radius for stable univalent and convex harmonic mappings, as well as stable univalent logharmonic mappings, and discusses improved inequalities and related radii.
Findings
Determined Bohr's radius for stable univalent harmonic mappings.
Established Bohr's radius for stable convex harmonic mappings.
Analyzed Bohr's Rogonsiski radius for these classes.
Abstract
We consider the class of \emph{stable} harmonic mappings introduced by Martin, Hernandez, and the class of \emph{stable} logharmonic mappings 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.
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Taxonomy
TopicsAnalytic and geometric function theory · Nonlinear Partial Differential Equations · Differential Equations and Boundary Problems